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A023146 Numbers k such that prime(k) == 4 (mod k).

%I A023146 #39 Feb 12 2021 05:22:31
%S A023146 1,75,77,637331,637333,637341,637343,27067053,179992917,8179002205,
%T A023146 2636913002917,6201265271239157,6201265271239347,6201265271239413,
%U A023146 6201265271239981,6201265271240331,6201265271240341,2159986889494445405,2159986889494445525,2159986889494445615
%N A023146 Numbers k such that prime(k) == 4 (mod k).
%e A023146 The 75th prime is 379 and 379 == 4 (mod 75). Hence 75 is in the sequence.
%e A023146 The 76th prime is 383, but 383 == 3, not 4, (mod 76). So 76 is not in the sequence.
%t A023146 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 *)
%t A023146 Select[Range[1000], Mod[Prime[#], #] == 4 &] (* _Alonso del Arte_, Nov 16 2018 *)
%o A023146 (Sage)
%o A023146 def A023146(max) :
%o A023146     terms = []
%o A023146     p = 2
%o A023146     for n in range(1, max+1) :
%o A023146         if (p - 4) % n == 0 : terms.append(n)
%o A023146         p = next_prime(p)
%o A023146     return terms
%o A023146 # _Eric M. Schmidt_, Feb 05 2013
%Y A023146 Cf. A171431, A092046.
%Y A023146 Cf. A023143, A023144, A023145, A023147, A023148, A023149, A023150, A023151, A023152.
%K A023146 nonn
%O A023146 1,2
%A A023146 _David W. Wilson_
%E A023146 More terms from _Robert G. Wilson v_, Feb 18 2004
%E A023146 2 more terms from _Giovanni Resta_ and _Robert G. Wilson v_, Feb 22 2006
%E A023146 First term inserted by _Eric M. Schmidt_, Feb 05 2013
%E A023146 a(11)-a(20) from _Giovanni Resta_, Feb 23 2020