A085515 Order of first occurrence of a sequence of exactly n consecutive primes of the form 6*k+1.

1, 2, 3, 6, 4, 5, 7, 8, 10, 11, 9, 13, 12, 15, 16, 14, 17, 18, 21, 19, 20, 23, 22, 25, 24, 26, 31, 27, 28, 30, 29, 32, 34, 33, 35

Offset

1,2

Comments

This sequence gives the index of A055625(n) after sorting by increasing magnitude.

Links

Table of n, a(n) for n=1..35.

J. K. Andersen, Consecutive Congruent Primes.

Hugo Pfoertner, Record producing runs of primes of the forms 6k+-1

Hugo Pfoertner, FORTRAN function ISPRIM to check primality.

Example

a(3)=3, a(4)=6, a(5)=4 because the first occurrence of exactly 6 consecutive primes of the form 6*k+1 (1741,1747,1753,1759,1777,1783) occurs after the first occurrence of 3 consecutive primes of this form (151,157,163) and before the first occurrence of 4 consecutive "6k+1"-primes (3049,3061,3067,3079).

Mathematica

(* Program not suitable to compute a large number of terms. *)
pp = Table[{p = Prime[n], Mod[p, 6]}, {n, 10^7}];
sp = Split[pp, Mod[#1[[2]], 6] == Mod[#2[[2]], 6]&];
b[n_] := SelectFirst[sp, Length[#] == n && MatchQ[#, {{_Integer, 1} ..}]& ][[1, 1]];
Sort[Table[{b[n], n}, {n, 1, 16}]][[All, 2]] (* Jean-François Alcover, Nov 21 2018 *)

Prog

FORTRAN program given at link.

Crossrefs

Cf. A055625, A085516 (sorted occurrence of first runs of "6k-1" primes).

Sequence in context: A132368 A157248 A368229 * A082354 A130344 A122344

Adjacent sequences: A085512 A085513 A085514 * A085516 A085517 A085518

Keyword

more,nonn

Author

Hugo Pfoertner, Jul 31 2003

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 27 2006

a(32)-a(35) from Giovanni Resta, Aug 04 2013

Status

approved