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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187785 Number of ways to write n=x+y (x,y>=0) with {6x-1,6x+1} a twin prime pair and y a triangular number 2
1, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 2, 4, 0, 2, 2, 3, 4, 1, 3, 1, 3, 3, 3, 2, 3, 2, 3, 2, 2, 4, 2, 7, 1, 3, 2, 1, 6, 4, 4, 3, 1, 3, 2, 3, 6, 3, 6, 0, 3, 3, 2, 6, 2, 4, 1, 3, 4, 3, 3, 4, 4, 1, 1, 1, 3, 3, 6, 2, 2, 2, 2, 7, 1, 3, 3, 2, 5, 2, 5, 2, 1, 5, 1, 4, 1, 4, 4, 1, 3, 2, 3, 4, 2, 3, 4, 2, 5, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: a(n)>0 for all n>48624 not equal to 76106.

We have verified this for n up to 2*10^8. It seems that 723662 is the unique n>76106 which really needs y=0 in the described representation.

Compare the conjecture with another Sun's conjecture associated with A132399.

REFERENCES

Zhi-Wei Sun, On sums of primes and triangular numbers, J. Comb. Number Theory 1(2009), no. 1, 65-76.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..100000

Zhi-Wei Sun, Conjectures involving primes and quadratic forms, arXiv:1211.1588.

EXAMPLE

a(9)=1 since 9=3+3(3+1)/2 with 6*3-1 and 6*3+1 both prime.

MATHEMATICA

a[n_]:=a[n]=Sum[If[PrimeQ[6(n-k(k+1)/2)-1]==True&&PrimeQ[6(n-k(k+1)/2)+1]==True, 1, 0], {k, 0, (Sqrt[8n+1]-1)/2}]

Do[Print[n, " ", a[n]], {n, 1, 100}]

CROSSREFS

Cf. A001097, A000217, A132399, A187759, A187757, A219157.

Sequence in context: A197169 A048052 A184156 * A238277 A258757 A024708

Adjacent sequences:  A187782 A187783 A187784 * A187786 A187787 A187788

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 06 2013

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 5 07:46 EDT 2020. Contains 335462 sequences. (Running on oeis4.)