A113568 Numbers k such that prime(k) +- k, prime(k) +- 2k, prime(k) +- 3k and prime(k) +- 4k are all primes.

2053380, 794006430, 1659273630, 3621510480, 3725013180, 4361365470, 4993201710, 7311363150, 7865614680, 9934880340, 10608361260, 12818200500, 13499311980, 13940598420, 14241904320, 14463052170, 14601895770, 18668815620, 19102545000, 20336611050, 20706006090, 21322649670, 22595831580

Offset

1,1

Links

Table of n, a(n) for n=1..23.

Mathematica

t = {}; p = 2*3*5*7; Do[ If[ PrimeQ[Prime[p*n] - p*3n] && PrimeQ[Prime[p*n] - p*2n] && PrimeQ[Prime[p*n] - p*n] && PrimeQ[Prime[p*n] + p*n] && PrimeQ[Prime[p*n] + p*2n] && PrimeQ[Prime[p*n] + p*3n], AppendTo[t, n]], {n, 17 106}]; p*t

Prog

(PARI) list(lim) = {my(k = 0, q); forprime(p = 1, lim, k++; q = 1; for(i = -4, 4, if(i != 0 && !isprime(p + i*k), q = 0; break)); if(q, print1(k, ", "))); } \\ Amiram Eldar, Jul 12 2025

Crossrefs

Cf. A064403, A112530, A113567.

Sequence in context: A034639 A206667 A251512 * A387885 A186915 A186907

Adjacent sequences: A113565 A113566 A113567 * A113569 A113570 A113571

Keyword

nonn

Author

Robert G. Wilson v, Sep 20 2005

Extensions

a(4)-a(23) from Amiram Eldar, Jul 12 2025

Status

approved