A185936 -id:A185936 - cp's OEIS frontend

A185938 First of a run of 3 or more consecutive primes which are congruent to 2 (mod 3).

47, 167, 251, 257, 503, 557, 587, 647, 941, 971, 1097, 1181, 1217, 1361, 1493, 1499, 1889, 1901, 1907, 2063, 2393, 2399, 2411, 2441, 2897, 2957, 3191, 3797, 4007, 4073, 4373, 4391, 4397, 4451, 4457, 4673, 4679, 4691, 4871, 5081, 5237, 5261, 5297, 5351, 5381, 5387, 5801, 6257, 6311, 6317, 6857, 6911, 6971, 7001, 7079

Offset: 1

M. F. Hasler, Feb 06 2011

nonn

The subsequence of terms A185935(k) such that nextprime(A185935(k))=A185935(k+1). If nextprime(a(n))=a(n+1), then a(n) is in A185941.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A185935, A185936, A185941.

Select[Partition[Prime[Range[1500]], 3, 1], Mod[#, 3] == {2, 2, 2} &][[All, 1]] (* Paolo Xausa, Mar 07 2025 *)

my(s=Mod([2,2,2],3), o=vector(#s), i=0); forprime( p=1,1e4, o[i++%3+1]=p; o-s || print1( o[(i+1)%3+1], ", "))

A185942 First of a run of 4 or more consecutive primes which all equal 1 (mod 3).

Original entry on oeis.org

1741, 1747, 1753, 3049, 3301, 4591, 5101, 6361, 7351, 7369, 8311, 8707, 8713, 8887, 9067, 9091, 9103, 9631, 10639, 11287, 12577, 12823, 12829, 13267, 15187, 15583, 15817, 15889, 15901, 16363, 16369, 16561, 16729, 16981, 17041, 17419, 17431, 17839, 18199, 18211, 19213, 19219, 19471, 19477, 19483, 19489, 20071

Offset: 1

M. F. Hasler, Feb 06 2011

nonn

Subsequence of terms of A185936 such that A185936(k+1) = nextprime(A185936(k)).

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A185934 - A185941.

mod3Q[l_]:=Union[Mod[#,3]&/@l]=={1}
Transpose[Select[Partition[Prime[Range[2500]],4,1],mod3Q]][[1]]  (* Harvey P. Dale, Feb 16 2011 *)

s=Mod([1,1,1,1],3);o=vector(#s);i=0;forprime(p=1,3e4,o[i++%#o+1]=p;o-s|print1(o[(i+1)%#o+1]","))

cp's OEIS Frontend

A185938 First of a run of 3 or more consecutive primes which are congruent to 2 (mod 3).

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