A023145 Numbers k such that prime(k) == 3 (mod k).

1, 2, 4, 7, 8, 31, 32, 34, 74, 76, 1052, 6455, 15928, 251707, 251765, 4124458, 27067012, 27067120, 69709718, 69709871, 69709877, 69709934, 69709943, 69709954, 69709963, 69709964, 465769810, 8179002124, 145935689390, 382465573486, 885992692751818, 885992692751822

Offset

1,2

Links

Giovanni Resta, Table of n, a(n) for n = 1..46

Example

204475053103 = prime(8179002124) and 204475053103 = 25*8179002124 + 3.

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 3, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
Select[Range[100000], Mod[Prime[#] - 3, #] == 0 &] (* T. D. Noe, Feb 05 2013 *)

Prog

(Sage)
def A023145(max) :
    terms = []
    p = 2
    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

Crossrefs

Cf. A171430, A092045, A023143, A023144, A023146, A023147, A023148, A023149, A023150, A023151, A023152.

Sequence in context: A122980 A012985 A291178 * A094446 A370003 A071790

Adjacent sequences: A023142 A023143 A023144 * A023146 A023147 A023148

Keyword

nonn

Author

David W. Wilson

Extensions

More terms from Robert G. Wilson v, Feb 18 2004

2 more terms from Giovanni Resta, Feb 22 2006

a(29) from Robert G. Wilson v, Feb 22 2006

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

Terms a(30) and beyond from Giovanni Resta, Feb 23 2020

Status

approved