A105287 Numbers k such that prime(k+1) == 2 (mod k).

1, 9, 67, 437, 441, 2615, 100349, 100353, 100359, 637197, 637305, 27066969, 27067049, 27067101, 27067113, 27067115, 179992839, 179993001, 55762149071, 382465573491

Offset: 1

Author

Zak Seidov, Apr 25 2005

Keywords

• nonn
• more

Comments

Integers k such that A004649(k+1) = 2. - Michel Marcus, Dec 30 2022

Crossrefs

Cf. A004649, A105286, A105288, A105290, A105329, A105451.

Programs

Mathematica

bb={};Do[If[2==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 200000}];bb
With[{nn=640000},Flatten[Position[Thread[{Range[nn],Prime[Range[2,nn+1]]}], ?(Mod[Last[#]-2,First[#]]==0&),{1},Heads->False]]] (* _Harvey P. Dale, Sep 23 2021 *)

Sage

def A105287(max) :
    terms = []
    p = 3
    for n in range(1, max+1) :
        if (p - 2) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

First term inserted by Eric M. Schmidt, Feb 05 2013

More terms from Harvey P. Dale, May 04 2013

a(12)-a(18) from Michel Marcus, Dec 29 2022

a(19)-a(20) from Max Alekseyev, Aug 31 2024