%I #30 Oct 23 2024 14:39:07
%S 2,3,3,2,2,11,2,3,7,7,2,3,11,5,647,2,5,23,79,239,823,2,5,29,19,647,
%T 233,6299,2,7,19,137,463,40427,1699,6287,2,7,31,251,11003,11617,
%U 102811,1697,150247,2,7,89,751,241,46187,11597,107507,10037,150239,2,7,89,241,947,1747,248987,11593,378023,67741,1610941
%N Square array read by antidiagonals in ascending order where T(n,k), n>1 and k>=1, is the least prime p, writtten in base n, starting a run of exactly k consecutive primes with non increasing sum of digits.
%e The prime numbers 7 and 11 are consecutive primes. In base 10, the sum of the digits of 7 and 11 are respectively 7 and 2. Since 7 is greater than or equal to 2, and there are no smaller numbers with this property, we have T(10,2) = 7.
%e The prime numbers 11, 13, 17 are consecutive primes. In base 2, the sum of the digits of 11 = 1011_2 and 13 = 1101_2 is 3 and the sum of digits of 17 = 10001_2 is 2. Since 3 >= 3 >= 2, and there are no smaller numbers with this property, we have T(2,3) = 11.
%e The top left corner of the array begins at T(2,1):
%e 2 3 11 7 647 823 ...
%e 3 2 7 5 239 233 ...
%e 2 3 11 79 647 40427 ...
%e 2 3 23 19 463 11617 ...
%e 2 5 29 137 11003 46187 ...
%e ... ... ... ... ... ... ...
%Y Cf. A007953.
%K tabl,nonn,base,new
%O 2,1
%A _Jean-Marc Rebert_, Oct 08 2024