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

%I A133277 #40 Oct 16 2024 21:25:31
%S A133277 2,2,3,3,5,7,5,11,17,23,5,11,17,23,29,7,37,67,97,127,157,7,157,307,
%T A133277 457,607,757,907,199,409,619,829,1039,1249,1459,1669,199,409,619,829,
%U A133277 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
%N A133277 Triangle read by rows: row n gives the arithmetic progression of n primes with minimal final term, cf. A005115.
%C A133277 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
%C A133277 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
%H A133277 OEIS wiki, <a href="/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.
%H A133277 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%e A133277 Triangle begins:
%e A133277     2;
%e A133277     2,   3;
%e A133277     3,   5,   7;
%e A133277     5,  11,  17,  23;
%e A133277     5,  11,  17,  23,   29;
%e A133277     7,  37,  67,  97,  127,  157;
%e A133277     7, 157, 307, 457,  607,  757,  907;
%e A133277   199, 409, 619, 829, 1039, 1249, 1459, 1669;
%e A133277   199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879;
%e A133277   199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089;
%e A133277   ...
%Y A133277 For common differences, see A093364. For initial terms, see A113827. For final terms, see A005115.
%Y A133277 Differs from A133276 (from T(11,1) = a(56) on).
%Y A133277 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).
%K A133277 nonn,tabl
%O A133277 1,1
%A A133277 _N. J. A. Sloane_, Oct 17 2007
%E A133277 A-numbers in the Name and Crossrefs sections corrected by _Bobby Jacobs_, Dec 10 2016
%E A133277 Name edited by _M. F. Hasler_, Jan 02 2020