A133277 - OEIS (original) (raw)

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

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

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).

EXTENSIONS

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