A096675 -id:A096675 - cp's OEIS frontend

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

Offset: 1

Lekraj Beedassy, Jul 09 2004

nonn

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

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

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 *)
2Select[ Range[450], PrimeQ[ # ] == PrimeQ[ # + 1] == PrimeQ[2# + 1, GaussianIntegers -> True] == False && PrimeQ[2# + 1] == True &] + 1 (* Robert G. Wilson v, Jul 11 2004 *)

nextcomposite(k)=if(k<3,4,if(isprime(k),k+1,k));
{m=440;n=4;while(nKlaus Brockhaus, Jul 11 2004

Equals 1 + 2*A096786.

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

A096786 Numbers n such that both n and n+1 are composite numbers that sum up to a Pythagorean prime (i.e., of the form 4k+1).

Original entry on oeis.org

8, 14, 20, 26, 44, 48, 50, 54, 56, 68, 74, 86, 90, 98, 114, 116, 120, 128, 134, 140, 146, 158, 168, 174, 176, 186, 194, 200, 204, 216, 224, 230, 254, 260, 278, 284, 288, 296, 300, 308, 320, 326, 338, 350, 354, 380, 384, 386, 398, 404, 410, 414, 426, 428, 440

Offset: 1

Lekraj Beedassy, Jul 09 2004

nonn

Subsequence (even numbers) of A096784. See A096785 for the associated primes.

Cf. A060254, A096784, A096785, A096787, A096788, A096675.

Select[ Range[450], PrimeQ[ # ] == PrimeQ[ # + 1] == PrimeQ[2# + 1, GaussianIntegers -> True] == False && PrimeQ[2# + 1] == True &] (* Robert G. Wilson v, Jul 11 2004 *)

nextcomposite(k)=if(k<3,4,if(isprime(k),k+1,k));
{m=465;n=4;while(nKlaus Brockhaus, Jul 11 2004

Equals (A096785 - 1)/2.

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

cp's OEIS Frontend

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

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions