A055623 First occurrence of run of primes congruent to 1 mod 4 of exactly length n.

5, 13, 89, 389, 2593, 12401, 77069, 262897, 11593, 373649, 766261, 3358169, 12204889, 18256561, 23048897, 12270077, 297387757, 310523021, 297779117, 3670889597, 5344989829, 1481666377, 2572421893, 1113443017, 121117598053, 84676452781, 790457451349, 3498519134533, 689101181569, 3289884073409

Offset

1,1

Comments

The term "exactly" means that before the first and after the last terms of the run, the next primes are not congruent to 1 modulo 4.

Carlos Rivera's Puzzle 256 includes Jack Brennen's a(29) starting at 689101181569 to 689101182437 and asks if anyone can break that 1999 record.

Links

Table of n, a(n) for n=1..30.

J. K. Andersen, Consecutive Congruent Primes.

Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 256, Jack Brennen old records

Formula

Compute sequence of primes congruent to 1 mod 4. When first occurrence of run of exactly length n is found, add first prime to sequence.

Example

a(3)=89 because here n=3 and 89 is the start of a run of exactly 3 consecutive primes congruent to 1 mod 4.
n=3: 83, 89, 97, 101, 103 are congruent to 3, 1, 1, 1, 3 modulo 4. So a(3) = 89.
a(33) = 3278744415797. - Jens Kruse Andersen, May 29 2006

Mathematica

nn = 10; t = Table[0, {nn}]; found = 0; p = 1; cnt = 0; While[found < nn, p = NextPrime[p]; If[Mod[p, 4] == 1, cnt++, If[0 < cnt <= nn && t[[cnt]] == 0, t[[cnt]] = NextPrime[p, -cnt]; found++]; cnt = 0]]; t (* T. D. Noe, Jun 21 2013 *)

Crossrefs

Cf. A055624, A055626.

Sequence in context: A081560 A057624 A092567 * A280294 A304663 A306167

Adjacent sequences: A055620 A055621 A055622 * A055624 A055625 A055626

Keyword

nonn

Author

Labos Elemer, Jun 05 2000

Extensions

Corrected and extended by Reiner Martin, Jul 18 2001

More terms from Jens Kruse Andersen, May 29 2006

Edited by N. J. A. Sloane, Jun 01 2006

Status

approved