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A117048 Prime numbers that are expressible as the sum of two positive triangular numbers. 7
2, 7, 11, 13, 29, 31, 37, 43, 61, 67, 73, 79, 83, 97, 101, 127, 137, 139, 151, 157, 163, 181, 191, 193, 199, 211, 227, 241, 263, 277, 281, 307, 331, 353, 367, 373, 379, 389, 409, 421, 433, 443, 461, 463, 487, 499, 541, 571, 577, 587, 601, 619, 631, 659, 661 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If the triangular number 0 is allowed, only one additional prime occurs: 3. In that case, the sequence becomes A117112.

A subsequence of A051533. - Wolfdieter Lang, Jan 11 2017

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

EXAMPLE

2 = 1 + 1

7 = 1 + 6

11 = 1 + 10

13 = 10 + 3, etc.

MATHEMATICA

tri = Table[n (n + 1)/2, {n, 40}]; Select[Union[Flatten[Outer[Plus, tri, tri]]], # <= tri[[-1]]+1 && PrimeQ[#] &] (* T. D. Noe, Apr 07 2011 *)

PROG

(PARI) is(n)=for(k=sqrtint(4*n+1)\2+1, (sqrtint(8*n+1)-1)\2, if(ispolygonal(n-k*(k+1)/2, 3), return(n>3 && isprime(n)))); n==2 \\ Charles R Greathouse IV, Nov 07 2014

CROSSREFS

Cf. A000040, A000217, A002243, A002244, A020756, A051533, A053614, A060773, A002636.

Sequence in context: A045369 A157975 A045370 * A040128 A209630 A235266

Adjacent sequences:  A117045 A117046 A117047 * A117049 A117050 A117051

KEYWORD

easy,nonn

AUTHOR

Andrew S. Plewe, Apr 15 2006

STATUS

approved

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Last modified April 21 20:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)