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A159071 Primes which are the sum of 6 consecutive triangular numbers A000217. 1
83, 251, 683, 1091, 2531, 5051, 7211, 11171, 15131, 16883, 18731, 21683, 24851, 29411, 33083, 42491, 59651, 85691, 107171, 109451, 114083, 133571, 138683, 151883, 160091, 189011, 201251, 204371, 236891, 268211, 271811, 297683, 309131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

Primes which are the sum of 3 consecutive odd squares A016754. [Alex Ratushnyak, Jul 24 2012]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

EXAMPLE

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

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

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

MATHEMATICA

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

Select[Table[3n^2+8, {n, 2, 1000}], PrimeQ] (* Vincenzo Librandi, Dec 02 2011 *)

PROG

(MAGMA) [a: n in [2..400] | IsPrime(a) where a is 3*n^2+8]; // Vincenzo Librandi, Dec 02 2011

CROSSREFS

Cf. A000217, A016754.

Sequence in context: A141933 A238680 A008897 * A023284 A142025 A142387

Adjacent sequences:  A159068 A159069 A159070 * A159072 A159073 A159074

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 04 2009

EXTENSIONS

11 removed, examples edited by R. J. Mathar, Apr 06 2009

STATUS

approved

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Last modified September 19 17:50 EDT 2020. Contains 337180 sequences. (Running on oeis4.)