A023146 - OEIS

A023146

Numbers k such that prime(k) == 4 (mod k).

1, 75, 77, 637331, 637333, 637341, 637343, 27067053, 179992917, 8179002205, 2636913002917, 6201265271239157, 6201265271239347, 6201265271239413, 6201265271239981, 6201265271240331, 6201265271240341, 2159986889494445405, 2159986889494445525, 2159986889494445615

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OFFSET

1,2

LINKS

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

EXAMPLE

The 75th prime is 379 and 379 == 4 (mod 75). Hence 75 is in the sequence.

The 76th prime is 383, but 383 == 3, not 4, (mod 76). So 76 is not in the sequence.

MATHEMATICA

nextPrime[n_] := Block[{k = n + 1}, While[!PrimeQ[k], k++]; k]; p = 1; Do[If[Mod[p = nextPrime[p], n] == 4, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)

Select[Range[1000], Mod[Prime[#], #] == 4 &] (* Alonso del Arte, Nov 16 2018 *)

PROG

(Sage)

def A023146(max) :

terms = []

p = 2

for n in range(1, max+1) :

if (p - 4) % n == 0 : terms.append(n)

p = next_prime(p)

return terms

# Eric M. Schmidt, Feb 05 2013

CROSSREFS