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

Author

David W. Wilson

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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

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