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

1,1

Links

Table of n, a(n) for n=1..105.

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

Formula

T(n,1) = 2.

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

Example

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.

Crossrefs

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

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

Sequence in context: A328577 A094321 A107789 * A348470 A317369 A096916

Adjacent sequences: A124061 A124062 A124063 * A124065 A124066 A124067

Keyword

nonn,tabf

Author

R. J. Mathar, Nov 04 2006

Extensions

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

Status

approved