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

1,2

Comments

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

Links

Table of n, a(n) for n=1..20.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A255877 A197277 A238317 * A163349 A016130 A115202

Adjacent sequences: A105284 A105285 A105286 * A105288 A105289 A105290

Keyword

nonn,more

Author

Zak Seidov, Apr 25 2005

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

Status

approved