The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182663 Number of ordered ways to write n = p + q with q > 0 such that p and 2*p + prime(q) are both prime. 1
 0, 0, 0, 1, 0, 2, 2, 2, 3, 3, 1, 1, 1, 3, 3, 5, 2, 2, 4, 1, 4, 4, 4, 3, 1, 3, 3, 3, 7, 4, 4, 2, 3, 1, 3, 5, 2, 2, 5, 6, 1, 6, 5, 2, 4, 6, 4, 3, 3, 4, 4, 6, 4, 3, 5, 2, 3, 5, 5, 2, 6, 3, 6, 5, 5, 4, 7, 4, 4, 8, 6, 6, 5, 5, 4, 8, 7, 6, 4, 4, 5, 6, 4, 5, 4, 3, 7, 9, 9, 4, 8, 5, 6, 2, 9, 6, 7, 1, 7, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Conjecture: (i) a(n) > 0 for all n > 5. (ii) Any integer n > 5 can be written as p + q (q > 0) with p and prime(p) + 2*q both prime. (iii) Each integer n > 10 can be written as p + q (q > 0) with p and prime(p)^2 + 4*q^2 both prime. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 EXAMPLE a(11) = 1 since 11 = 5 + 6 with 5 and 2*5 + prime(6) = 10 + 13 = 23 both prime. a(98) = 1 since 98 = 19 + 79 with 19 and 2*19 + prime(79) = 38 + 401 = 439 both prime. MATHEMATICA p[n_, m_]:=PrimeQ[2*m+Prime[n-m]] a[n_]:=Sum[If[p[n, Prime[k]], 1, 0], {k, 1, PrimePi[n-1]}] Table[a[n], {n, 1, 100}] CROSSREFS Cf. A000040, A182662, A236831. Sequence in context: A125600 A084053 A331553 * A071452 A282495 A341421 Adjacent sequences:  A182660 A182661 A182662 * A182664 A182665 A182666 KEYWORD nonn AUTHOR Zhi-Wei Sun, Feb 01 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 12 11:30 EDT 2021. Contains 342920 sequences. (Running on oeis4.)
The text passage is a description of a sequence from the Online Encyclopedia of Integer Sequences (OEIS), including its definition, examples, and Mathematica code for generating the sequence.
no_question

the passage does not contain any explicit mathematical question or problem to solve. it provides a definition and examples of a sequence, but does not ask the reader to perform any calculations or solve any problems.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182663 Number of ordered ways to write n = p + q with q > 0 such that p and 2*p + prime(q) are both prime. 1
 0, 0, 0, 1, 0, 2, 2, 2, 3, 3, 1, 1, 1, 3, 3, 5, 2, 2, 4, 1, 4, 4, 4, 3, 1, 3, 3, 3, 7, 4, 4, 2, 3, 1, 3, 5, 2, 2, 5, 6, 1, 6, 5, 2, 4, 6, 4, 3, 3, 4, 4, 6, 4, 3, 5, 2, 3, 5, 5, 2, 6, 3, 6, 5, 5, 4, 7, 4, 4, 8, 6, 6, 5, 5, 4, 8, 7, 6, 4, 4, 5, 6, 4, 5, 4, 3, 7, 9, 9, 4, 8, 5, 6, 2, 9, 6, 7, 1, 7, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Conjecture: (i) a(n) > 0 for all n > 5. (ii) Any integer n > 5 can be written as p + q (q > 0) with p and prime(p) + 2*q both prime. (iii) Each integer n > 10 can be written as p + q (q > 0) with p and prime(p)^2 + 4*q^2 both prime. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 EXAMPLE a(11) = 1 since 11 = 5 + 6 with 5 and 2*5 + prime(6) = 10 + 13 = 23 both prime. a(98) = 1 since 98 = 19 + 79 with 19 and 2*19 + prime(79) = 38 + 401 = 439 both prime. MATHEMATICA p[n_, m_]:=PrimeQ[2*m+Prime[n-m]] a[n_]:=Sum[If[p[n, Prime[k]], 1, 0], {k, 1, PrimePi[n-1]}] Table[a[n], {n, 1, 100}] CROSSREFS Cf. A000040, A182662, A236831. Sequence in context: A125600 A084053 A331553 * A071452 A282495 A341421 Adjacent sequences:  A182660 A182661 A182662 * A182664 A182665 A182666 KEYWORD nonn AUTHOR Zhi-Wei Sun, Feb 01 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 12 11:30 EDT 2021. Contains 342920 sequences. (Running on oeis4.)
user
The text passage is a description of a sequence from the Online Encyclopedia of Integer Sequences (OEIS), including its definition, examples, and Mathematica code for generating the sequence.

TYPE: NO_QUESTION

The passage does not contain any explicit mathematical question or problem to solve. It provides a definition and examples of a sequence, but does not ask the reader to perform any calculations or solve any problems.