A067185 Numbers k such that prime(k+1) + prime(k) == 1 (mod k).

1, 7, 17, 109, 281, 1669, 6592663, 16899113, 16899145, 16899295, 749973611, 5067034877, 5067034925, 34487825911, 1626582230375

Offset: 1

Author

Benoit Cloitre, Feb 19 2002

Keywords

• nonn
• more

Crossrefs

Cf. A066895 (== 0 instead of 1).

Programs

Mathematica

a = b = 0; Do[b = Prime[n + 1]; If[Mod[a + b, n] == 1, Print[n]]; a = b, {n, 1, 10^9}]

PARI

isok(k) = (prime(k+1) + prime(k)) % k == 1; \\ Michel Marcus, Feb 17 2021

Sage

def A067185(max):
    terms = []
    p = 2
    for n in range(1, max + 1):
        q = next_prime(p)
        if not (p + q - 1) % n:
            terms.append(n)
        p = q
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

Edited and extended by Robert G. Wilson v, Feb 19 2002

Extended by David W. Wilson, Feb 20 2002

a(11)-a(14) from Donovan Johnson, Mar 10 2010

First term from Eric M. Schmidt, Feb 05 2013