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A124064
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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.
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| R. J. Mathar, Table for d <= 1000 (PDF)
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FORMULA
| T(n,1) = 2.
lim n->inf (a(n)/n) = SUM(p prime; (p-1)/(#(p-1)) = 2.92005097731613471209+
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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.
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CROSSREFS
| Assuming the k-tuples conjecture, A123556 gives lengths of table rows.
Sequence in context: A081414 A094321 A107789 * A096916 A098014 A059957
Adjacent sequences: A124061 A124062 A124063 * A124065 A124066 A124067
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KEYWORD
| nonn,tabf
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AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 04 2006
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EXTENSIONS
| Edited by David W. Wilson, Nov 05 2006 and Nov 25 2006
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