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A096785
Primes of form 4k+1 which are the sum of two consecutive composite numbers.
12
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
1,1
FORMULA
Equals 1 + 2*A096786.
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 *)
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.
Sequence in context: A103739 A255871 A196668 * A104228 A049484 A274465
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Jul 09 2004
EXTENSIONS
Corrected and extended by Klaus Brockhaus, Rick L. Shepherd and Ray Chandler, Jul 10 2004
STATUS
approved