cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A125025 Lengths of rows in A124570.

Original entry on oeis.org

3, 8, 3, 8, 3
Offset: 1

Views

Author

Jonathan Vos Post, Nov 15 2006

Keywords

Comments

This sequence is to A124570 as A123556 is to A124064.
a(n) is at most A053669(n)^2, with equality if and only if A053669(n)^2 is the first semiprime in the corresponding arithmetic progression. - Charlie Neder, Jan 10 2019
By subsampling a given arithmetic progression with k terms and distance d one may generate an arithmetic progression of a larger distance d*b, b=1,2,3...., with 1+(k-1)/b terms: a(b*n) >= 1+floor( (a(n)-1)/b ), b=1,2,3..... - R. J. Mathar, Aug 02 2021
18 <= a(6) <= 24. - Jinyuan Wang, Aug 06 2021
a(12) >= 17. a(18) >= 18. a(24) >= 18. a(30) >= 21. a(36) >= 19. a(42) >= 20. a(6006) >= 24 (starting 652744562555081). Hugo van der Sanden, Aug 14 2021

Crossrefs

Cf. A001358, A123556, A124064, A124570, A091016 (for n=6).

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.

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Nov 04 2006

Keywords

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

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

A091016 a(n) is the least x such that the n values x+0, x+6, x+12, ..., x+6*(n-1) are all products of exactly two primes (i.e., semiprimes).

Original entry on oeis.org

4, 4, 9, 203, 1333, 1333, 1333, 2159, 8309, 18799, 60499, 60499, 186779, 186779, 186779, 12015573923, 12015573923, 6763513182767
Offset: 1

Views

Author

Don Reble, Feb 25 2004

Keywords

Comments

a(19) > 1.e14 if it exists. - Hugo van der Sanden, Aug 06 2021

Examples

			a(4)=203 because 203 = 7*29, 209 = 11*19, 215 = 5*43, 221 = 13*17.

Crossrefs

Cf. A082919, A092129. Row 6 of A124570.

Extensions

a(8) and a(9) corrected and a(18) from Donovan Johnson, Oct 01 2010
Showing 1-3 of 3 results.

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