A105288 Numbers k such that prime(k+1) == 3 (mod k).

1, 2, 4, 5, 70, 440, 1055, 1058, 6461, 6466, 6469, 251752, 4124468, 27067036, 27067112, 69709709, 69709957, 465769835, 8179002104, 145935689357, 382465573490

Offset: 1

Author

Zak Seidov, Apr 25 2005

Keywords

• nonn
• more

Comments

Integers k such that A004649(k+1) = 3. - Michel Marcus, Dec 30 2022

Crossrefs

Cf. A004649, A105286, A105287, A105290, A105329, A105451.

Programs

Magma

[1,2] cat [n: n in [1..2*10^4] | NthPrime(n+1) mod n eq 3]; // Vincenzo Librandi, May 02 2018

Maple

n:= 0: p:= 2: count:= 0:
for n from 1 while count < 13 do
p:= nextprime(p);
if p-3 mod n = 0 then
    count:= count+1;
  A[count]:= n;
  fi
od:
seq(A[i],i=1..count); # Robert Israel, May 02 2018

Mathematica

bb={};Do[If[3==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 200000}];bb
Join[{1, 2}, Select[Range[2 10^7], Mod[Prime[# + 1], #]==3 &]] (* Vincenzo Librandi, May 02 2018 *)

Sage

def A105288(max) :
    terms = []
    p = 3
    for n in range(1, max+1) :
        if (p - 3) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

First two terms inserted by Eric M. Schmidt, Feb 05 2013

a(12)-a(13) from Robert Israel, May 02 2018

a(14)-a(21) from Giovanni Resta, May 02 2018