A096453 Primes p such that the number of primes q, 5 <= q < p, congruent to 1 mod 3, is two less than the number of such primes congruent to 2 mod 3.

31, 59, 67, 73, 97, 103, 109, 127, 137, 149, 157, 179, 191, 197, 211, 241, 257, 347, 353, 379, 389, 401, 419, 431, 439, 449, 461, 467, 761, 773, 797, 1787, 1801, 1823, 1847, 1867, 1873, 1879, 1901, 3761, 9203, 198479, 198593, 608981812531, 608981812651, 608981812697

Offset

1,1

Comments

Primes prime(n) such that A112632(n-1) = 3. In other words, p >= 5 such that A321856(prevprime(p)) = 3. - Jianing Song, Jan 06 2026

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Maple

ct := -2: q:=2: for n from 2 to 20000 do p:=q: q:=ithprime(n): ct:=ct+`if`(p mod 3 = 1, -1, 1): if(ct=2)then printf("%d, ", q): fi: od: # Nathaniel Johnston, Jun 16 2011

Mathematica

npc1Q[n_]:=Module[{tot=PrimePi[n]-3, c}, c=Count[Prime[Range[3, tot+2]], _?(Mod[ #, 3]==1&)]; c==tot/2-1]; Select[Prime[Range[18000]], npc1Q] (* Harvey P. Dale, Aug 22 2013 *)

Prog

(PARI) lista(limit=10^6)={my(c=2); forprime(p=5, limit, if(!c, print1(p, ", ")); if(p%3==1, c++, c--))} \\ Andrew Howroyd, Aug 09 2025

Crossrefs

Sequence of the same family: A096452, A096453.

See also A096447, A096448, A096451, A096450, A096454, A096455.

Sequence in context: A220539 A193362 A293345 * A218794 A218771 A109356

Adjacent sequences: A096450 A096451 A096452 * A096454 A096455 A096456

Keyword

nonn

Author

Yasutoshi Kohmoto, Aug 12 2004

Extensions

More terms and better definition from Joshua Zucker, May 21 2006

a(44) onwards from Andrew Howroyd, Aug 09 2025

Status

approved