A124064 Table read by rows: T(d,k) (d >= 1, k >= 1) = smallest prime p of k (not necessarily consecutive) primes in arithmetic progression with common difference d.

2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 5, 5, 5, 5, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 5, 5, 5, 5, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 5, 5, 5, 2, 2, 3, 3, 2, 2, 2, 7, 2, 2, 5, 5, 59, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 7, 7, 7, 7, 7, 2, 2, 5, 2, 2, 3, 3, 2, 2, 2, 5, 7, 31, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 5, 5, 5, 5

Offset: 1

Author

R. J. Mathar, Nov 04 2006

Keywords

• nonn
• tabf

Examples

			Table begins:
d \k|..1..2..3..4..5..
----+-----------------
..1.|..2..2
..2.|..2..3..3
..3.|..2..2
..4.|..2..3..3
..5.|..2..2
..6.|..2..5..5..5..5
..7.|..2
..8.|..2..3..3
..9.|..2..2
.10.|..2..3..3
.11.|..2..2
.12.|..2..5..5..5..5
.13.|..2
.14.|..2..3..3
.15.|..2..2
.16.|..2..3
.17.|..2..2
.18.|..2..5..5..5
.19.|..2
.20.|..2..3..3
T(24,4) = 59 since (59,83,107,131) is the first A.P. of 4 primes with difference 24.
		

Links

• R. J. Mathar, Table for d <= 1000 (PDF)

Crossrefs

Cf. A087242 (column k=2), A124570 (semiprimes analog), A249207.

Assuming the k-tuples conjecture, A123556 gives lengths of table rows.

Formula

T(n,1) = 2.

lim n->inf (a(n)/n) = SUM(p prime; (p-1)/(#(p-1)) = 2.92005097731613471209+

Extensions

Edited by David W. Wilson, Nov 05 2006 and Nov 25 2006