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A117048 Prime numbers that are expressible as the sum of two positive triangular numbers. 7

%I #18 Sep 24 2018 16:53:14

%S 2,7,11,13,29,31,37,43,61,67,73,79,83,97,101,127,137,139,151,157,163,

%T 181,191,193,199,211,227,241,263,277,281,307,331,353,367,373,379,389,

%U 409,421,433,443,461,463,487,499,541,571,577,587,601,619,631,659,661

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

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

%C A subsequence of A051533. - _Wolfdieter Lang_, Jan 11 2017

%H T. D. Noe, <a href="/A117048/b117048.txt">Table of n, a(n) for n = 1..10000</a>

%e 2 = 1 + 1

%e 7 = 1 + 6

%e 11 = 1 + 10

%e 13 = 10 + 3, etc.

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

%K easy,nonn

%O 1,1

%A _Andrew S. Plewe_, Apr 15 2006

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)