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A159071 Primes which are the sum of 6 consecutive triangular numbers A000217. 1

%I #21 Sep 08 2022 08:45:43

%S 83,251,683,1091,2531,5051,7211,11171,15131,16883,18731,21683,24851,

%T 29411,33083,42491,59651,85691,107171,109451,114083,133571,138683,

%U 151883,160091,189011,201251,204371,236891,268211,271811,297683,309131

%N Primes which are the sum of 6 consecutive triangular numbers A000217.

%C Primes of the form 3*k^2 + 18*k + 35 = 3*(k+3)^2 + 8, k >= 0. [_R. J. Mathar_, Apr 06 2009]

%C Primes which are the sum of 3 consecutive odd squares A016754. [_Alex Ratushnyak_, Jul 24 2012]

%H Vincenzo Librandi, <a href="/A159071/b159071.txt">Table of n, a(n) for n = 1..5000</a>

%e 83 = A000040(23) = Sum_{i=2..7} A000217(i).

%e 251 = A000040(54) = Sum_{i=6..11} A000217(i).

%e 683 = A000040(124) = Sum_{i=12..17) A000217(i).

%t tr[a_]:=Module[{x},s=0;If[a<0,b=Abs[a]+1,b=a];For[i=1,i<b,s+=i;i++ ]; x=s]; lst={};Do[a1=tr[n];b1=tr[n+1];c1=tr[n+2];d1=tr[n+3];e1=tr[n+4]; f1=tr[n+5];p=a1+b1+c1+d1+e1+f1;If[PrimeQ[p],AppendTo[lst,p]],{n,-2, 6!}];lst

%t Select[Table[3n^2+8,{n,2,1000}],PrimeQ] (* _Vincenzo Librandi_, Dec 02 2011 *)

%o (Magma) [a: n in [2..400] | IsPrime(a) where a is 3*n^2+8]; // _Vincenzo Librandi_, Dec 02 2011

%Y Cf. A000217, A016754.

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 04 2009

%E 11 removed, examples edited by _R. J. Mathar_, Apr 06 2009

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)