A133276 - OEIS

%I #18 Jan 03 2020 10:19:26

%S 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 457,607,757,907,199,409,619,829,1039,1249,1459,1669,199,409,619,829,

%U 1039,1249,1459,1669,1879,199,409,619,829,1039,1249,1459,1669,1879,2089,60858179,60860489,60862799,60865109,60867419,60869729,60872039,60874349,60876659,60878969,60881279

%N Triangle read by rows: row n gives the first arithmetic progression of n primes with minimal distance, cf. A033188.

%C The first 10 rows (i.e., 55 terms) are the same as for A133277 (where the final term is minimal), but here a(56) = T(11,1) = 608581797 while A133277(11,1) = 110437. - _M. F. Hasler_, Jan 02 2020

%H OEIS wiki, <a href="https://oeis.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.

%H <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>

%e Triangle begins:

%e     2

%e     2   3

%e     3   5   7

%e     5  11  17  23

%e     5  11  17  23   29

%e     7  37  67  97  127  157

%e     7 157 307 457  607  757  907

%e   199 409 619 829 1039 1249 1459 1669

%e   199 409 619 829 1039 1249 1459 1669 1879

%e   199 409 619 829 1039 1249 1459 1669 1879 2089

%e   ...

%e Row 10 is the same as in A086786, A113470, A133277, and listed as A033168. - _M. F. Hasler_, Jan 02 2020

%p AP:=proc(i,d,l) [seq(i + (j-1)*d, j=1..l )]; end;

%Y For common differences see A033188, for initial terms see A033189.

%Y Different from A133277 (from T(11,1) = a(56) on).

%Y Cf. A086786, A113470, A033168.

%K nonn,tabl

%O 1,1

%A _N. J. A. Sloane_, Oct 17 2007