A092740 Primes p such that p^2 - 1 is the sum of two consecutive primes.

3, 5, 11, 17, 19, 29, 43, 53, 79, 101, 113, 127, 137, 179, 251, 281, 349, 409, 419, 431, 449, 521, 569, 571, 577, 599, 643, 661, 677, 739, 797, 823, 853, 857, 883, 907, 941, 991, 1009, 1049, 1087, 1091, 1129, 1163, 1181, 1259, 1289, 1381, 1451, 1459, 1489

Offset

1,1

Links

Zak Seidov, Table of n, a(n) for n = 1..1200

Example

Sequence contains the prime 3 because 3+5+1 = 3^2, the prime 5 because 11+13+1 = 5^2, the prime 11 because 59+61+1 = 11^2, the prime 17 because 139+149+1 = 17^2, etc.

Maple

seq( ifactor(ithprime(x)+ithprime(x+1)+1), x=1..20); # check squares of primes

Mathematica

f[n_] := Block[{k = Prime[n] + Prime[n + 1] + 1}, If[IntegerQ[ Sqrt[k]], k, 0]]; Select[ Sqrt[ f[ # ]] & /@ Select[ Range[10000], f[ # ] != 0 &], PrimeQ[ # ] &] (* Robert G. Wilson v, Apr 15 2004 *)
tspQ[n_]:=Module[{c=n^2-1}, NextPrime[c/2]+NextPrime[c/2, -1]==c]; Select[ Prime[ Range[250]], tspQ] (* Harvey P. Dale, Apr 30 2019 *)

Prog

(PARI) is(n) = precprime((n-1)/2)+nextprime(n/2) == n; \\ A001043
isok(p) = isprime(p) && is(p^2-1); \\ Michel Marcus, Mar 16 2019

Crossrefs

Cf. A001043, A045408.

Sequence in context: A279767 A125631 A045408 * A214296 A045409 A191206

Adjacent sequences: A092737 A092738 A092739 * A092741 A092742 A092743

Keyword

nonn

Author

Jorge Coveiro, Apr 12 2004

Extensions

Edited by Robert G. Wilson v and Don Reble, Apr 15 2004

Status

approved