cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A117048 Prime numbers that are expressible as the sum of two positive triangular numbers.

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%I A117048 #18 Sep 24 2018 16:53:14
%S A117048 2,7,11,13,29,31,37,43,61,67,73,79,83,97,101,127,137,139,151,157,163,
%T A117048 181,191,193,199,211,227,241,263,277,281,307,331,353,367,373,379,389,
%U A117048 409,421,433,443,461,463,487,499,541,571,577,587,601,619,631,659,661
%N A117048 Prime numbers that are expressible as the sum of two positive triangular numbers.
%C A117048 If the triangular number 0 is allowed, only one additional prime occurs: 3. In that case, the sequence becomes A117112.
%C A117048 A subsequence of A051533. - _Wolfdieter Lang_, Jan 11 2017
%H A117048 T. D. Noe, <a href="/A117048/b117048.txt">Table of n, a(n) for n = 1..10000</a>
%e A117048 2 = 1 + 1
%e A117048 7 = 1 + 6
%e A117048 11 = 1 + 10
%e A117048 13 = 10 + 3, etc.
%t A117048 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 *)
%o A117048 (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
%Y A117048 Cf. A000040, A000217, A002243, A002244, A020756, A051533, A053614, A060773, A002636.
%K A117048 easy,nonn
%O A117048 1,1
%A A117048 _Andrew S. Plewe_, Apr 15 2006