A096785 Primes of form 4k+1 which are the sum of two consecutive composite numbers.

17, 29, 41, 53, 89, 97, 101, 109, 113, 137, 149, 173, 181, 197, 229, 233, 241, 257, 269, 281, 293, 317, 337, 349, 353, 373, 389, 401, 409, 433, 449, 461, 509, 521, 557, 569, 577, 593, 601, 617, 641, 653, 677, 701, 709, 761, 769, 773, 797, 809, 821, 829, 853, 857, 881, 929, 937, 941, 953, 977

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

Equals 1 + 2*A096786.

Maple

select(n -> isprime(n) and not isprime((n+1)/2), [seq(i, i=5..1000, 4)]); # Robert Israel, Jul 02 2026

Mathematica

Do[If[PrimeQ[2*n+1]&&Equal[Mod[s, 4], 1]&&!PrimeQ[n]&&!PrimeQ[n+1], Print[2*n+1]], {n, 1, 1000}] (* Labos Elemer *)
(* Alternative: *)
2Select[ Range[450], PrimeQ[ # ] == PrimeQ[ # + 1] == PrimeQ[2# + 1, GaussianIntegers -> True] == False && PrimeQ[2# + 1] == True &] + 1 (* Robert G. Wilson v, Jul 11 2004 *)

Prog

(PARI) nextcomposite(k)=if(k<3, 4, if(isprime(k), k+1, k));
{m=440; n=4; while(n<m, k=nextcomposite(n+1); p=n+k; if(k==n+1&&isprime(p)&&p%4==1, print1(p, ", ")); n=k)} \\ Klaus Brockhaus, Jul 11 2004

Crossrefs

Subsequence of A060254. See A096786 for values 2n. See A096675 for n values.

Cf. A060254, A096784, A096786, A096787, A096788, A096675, A096678.

Sequence in context: A103739 A255871 A196668 * A104228 A049484 A274465

Adjacent sequences: A096782 A096783 A096784 * A096786 A096787 A096788

Keyword

nonn,changed

Author

Lekraj Beedassy, Jul 09 2004

Extensions

Corrected and extended by Klaus Brockhaus, Rick L. Shepherd and Ray Chandler, Jul 10 2004

More terms from Robert Israel, Jul 02 2026

Status

approved