A133277 Triangle read by rows: row n gives the arithmetic progression of n primes with minimal final term, cf. A005115.

2, 2, 3, 3, 5, 7, 5, 11, 17, 23, 5, 11, 17, 23, 29, 7, 37, 67, 97, 127, 157, 7, 157, 307, 457, 607, 757, 907, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089, 110437, 124297, 138157, 152017, 165877, 179737, 193597, 207457, 221317, 235177, 249037

Offset

1,1

Comments

The first 10 rows (i.e., 55 terms) are the same as for A133276 (where the common distance is minimal), but here T(11,1) = a(56) = 110437 while A133276(11,1) = 60858179. - M. F. Hasler, Jan 02 2020

For any prime p there is a p-AP (arithmetic progression of p primes) starting with p, where the common distance is given by A088430. For n between prime(k-1) and prime(k), there may be an n-AP starting at prime(k) (but not earlier) with a smaller common distance, given in A061558. - M. F. Hasler, Sep 17 2024

Links

Table of n, a(n) for n=1..66.

OEIS wiki, Primes in arithmetic progression.

Index entries for sequences related to primes in arithmetic progressions

Example

Triangle begins:
    2;
    2,   3;
    3,   5,   7;
    5,  11,  17,  23;
    5,  11,  17,  23,   29;
    7,  37,  67,  97,  127,  157;
    7, 157, 307, 457,  607,  757,  907;
  199, 409, 619, 829, 1039, 1249, 1459, 1669;
  199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879;
  199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089;
  ...

Crossrefs

For common differences, see A093364. For initial terms, see A113827. For final terms, see A005115.

Differs from A133276 (from T(11,1) = a(56) on).

See also A061558 (distance in earliest n-AP), A088430 (same for primes), A231017 (second term in p-AP starting with p), A061558 (distance of n-AP starting at the smallest possible prime).

Sequence in context: A322787 A391880 A130791 * A133276 A354485 A055501

Adjacent sequences: A133274 A133275 A133276 * A133278 A133279 A133280

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 17 2007

Extensions

A-numbers in the Name and Crossrefs sections corrected by Bobby Jacobs, Dec 10 2016

Name edited by M. F. Hasler, Jan 02 2020

Status

approved