A348835 - OEIS

%I #12 Mar 03 2024 17:19:43

%S 1,3,1,5,3,1,7,5,3,1,11,11,7,5,1,13,11,11,7,3,1,17,17,13,11,7,5,1,19,

%T 17,17,13,11,7,3,1,23,23,19,17,13,11,7,5,1,29,29,29,23,19,17,13,11,7,

%U 1,31,29,29,29,23,19,17,13,11,3,1,37,37,37,31,29,29,23,19,17,11,7,1

%N Triangle, read by rows, T(n, k) is the smallest term of A006005 strictly larger than abs(A006005(n) - A006005(k)).

%H Raghavendra Bhat, <a href="https://arxiv.org/abs/2110.14716">An Abelian Loop for Non-Composites</a>, arXiv:2110.14716 [math.GM], 2021.

%F T(n, n) = 1.

%F T(n, 1) = n.

%e Triangle begins:

%e    1;

%e    3,  1;

%e    5,  3,  1;

%e    7,  5,  3,  1;

%e   11, 11,  7,  5, 1;

%e   13, 11, 11,  7, 3, 1;

%e   17, 17, 13, 11, 7, 5, 1;

%e   ...

%o (PARI) f(n) = prime(n)-(n==1); /* A006005 */

%o T(n, k) = {my(j=1, m = abs(f(n)-f(k))); while (f(j) < m, j++); f(j);}

%Y Cf. A006005 (1 and the odd primes).

%K nonn,tabl

%O 1,2

%A _Michel Marcus_, Nov 01 2021