A023145 - OEIS

%I #31 Feb 11 2021 22:53:47

%S 1,2,4,7,8,31,32,34,74,76,1052,6455,15928,251707,251765,4124458,

%T 27067012,27067120,69709718,69709871,69709877,69709934,69709943,

%U 69709954,69709963,69709964,465769810,8179002124,145935689390,382465573486,885992692751818,885992692751822

%N Numbers k such that prime(k) == 3 (mod k).

%H Giovanni Resta, <a href="/A023145/b023145.txt">Table of n, a(n) for n = 1..46</a>

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

%t 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 *)

%t Select[Range[100000], Mod[Prime[#] - 3, #] == 0 &] (* _T. D. Noe_, Feb 05 2013 *)

%o (Sage)

%o def A023145(max) :

%o     terms = []

%o     p = 2

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

%o         if (p - 3) % n == 0 : terms.append(n)

%o         p = next_prime(p)

%o     return terms

%o # _Eric M. Schmidt_, Feb 05 2013

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

%K nonn

%O 1,2

%A _David W. Wilson_

%E More terms from _Robert G. Wilson v_, Feb 18 2004

%E 2 more terms from _Giovanni Resta_, Feb 22 2006

%E a(29) from _Robert G. Wilson v_, Feb 22 2006

%E First two terms inserted by _Eric M. Schmidt_, Feb 05 2013

%E Terms a(30) and beyond from _Giovanni Resta_, Feb 23 2020