A283145 a(1)=5; for n > 1, and a(n) is the least prime p > a(n-1) such that both q = p + 2n and r = q + 2n + 2 are prime.

5, 7, 17, 23, 31, 41, 53, 67, 71, 89, 127, 149, 173, 199, 251, 281, 283, 347, 383, 409, 461, 479, 523, 593, 641, 691, 719, 773, 823, 887, 971, 1033, 1097, 1163, 1231, 1301, 1373, 1447, 1619, 1709, 1741, 1823, 1907

Offset

1,1

Comments

Note that p,q,r are not required to be consecutive primes.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(1)=5 because both 5 + 2 = 7 and 7 + 4 = 11 are prime;
n=2: d=4, p=7 because both p + d = 11 and 11 + 6 = 17 are prime;
n=3: d=6: primes 11,13 are not qualified while 17 + 6 = 23 and 23 + 8 = 31 are prime hence a(3)=17.

Mathematica

m=0; p=3; s={}; Do[p = NextPrime[p]; m=m+2; While[!PrimeQ[p+m]||!PrimeQ[p+2*m+2], p=NextPrime[p]]; AppendTo[s, p], {50}]; s

Prog

(PARI) first(n)=my(v=vector(n), k=4); v[1]=5; forprime(p=5, , if(isprime(p+k) && isprime(p+2*k+2), v[k/2]=p; if(k==2*n, return(v)); k+=2)) \\ Charles R Greathouse IV, Mar 01 2017

Crossrefs

Cf. A283159.

Sequence in context: A044966 A359297 A283159 * A191145 A145354 A214345

Adjacent sequences: A283142 A283143 A283144 * A283146 A283147 A283148

Keyword

nonn

Author

Zak Seidov, Mar 01 2017

Extensions

a(16)-a(17) corrected by Charles R Greathouse IV, Mar 01 2017

Status

approved