A055624 First occurrence of run of primes congruent to 3 mod 4 of exactly length n.

3, 7, 739, 199, 883, 13127, 463, 36551, 39607, 183091, 4468903, 6419299, 241603, 11739307, 9177431, 95949311, 105639091, 341118307, 1800380579, 727334879, 9449915743, 1786054147, 22964264027, 54870713243, 79263248027, 454648144571, 722204126767, 1749300591127, 5070807638111, 8858854801319, 6425403612031, 113391385603

Offset: 1

Author

Labos Elemer, Jun 05 2000

Keywords

• easy
• nonn

Comments

The term "exactly" means that before the first and after the last terms of chain, the immediate primes are not congruent to 3 modulo 4.

Carlos Rivera's Puzzle 256 includes Jack Brennen's a(24) starting at 1602195714419 to 1602195715423 and asks if anyone can break that 1999 record.

Examples

			a(3)=739 because here n=3 and 739 is the start of a run of exactly 3 consecutive primes congruent to 3 mod 4.
		

Links

• J. K. Andersen, Consecutive Congruent Primes.
• Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 256, Jack Brennen old records

Crossrefs

Cf. A092567, A055623, A055626.

Formula

Compute sequence of primes congruent to 3 mod 4. When first occurrence of run of exactly length n is found, add first prime to sequence.

Extensions

More terms from Reiner Martin, Jul 18 2001

More terms from Jens Kruse Andersen, May 29 2006

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