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A375117 Irregular triangle of positive integers, read by rows, the elements of the n-th row being the nonzero remainders, in increasing order, when the Euclidean algorithm is applied to 2^n-1 and n.

%I A375117 #24 Aug 18 2024 20:44:34
%S A375117 1,1,1,3,1,3,1,1,7,1,2,7,1,3,1,3,1,1,2,3,1,7,1,15,1,9,1,5,15,7,1,3,1,
%T A375117 3,6,9,15,1,6,1,2,3,1,2,25,1,2,13,15,1,3,1,1,31,1,2,5,7,1,3,1,17,9,27,
%U A375117 1,1,2,3,1,3,4,7,5,10,15,1,21,1,1,14,15,1,3,13,16
%N A375117 Irregular triangle of positive integers, read by rows, the elements of the n-th row being the nonzero remainders, in increasing order, when the Euclidean algorithm is applied to 2^n-1 and n.
%e A375117 The triangle begins:
%e A375117     1;
%e A375117     1;
%e A375117     1, 3;
%e A375117     1;
%e A375117     3;
%e A375117     1;
%e A375117     1, 7;
%e A375117     1, 2, 7;
%e A375117     1, 3;
%e A375117     1;
%e A375117     3;
%e A375117     1;
%e A375117     3;
%e A375117     ...
%e A375117 Row(2) is {1}, because 2^2-1 = 4-1 = 3, and 3 divided by 2 leaves a remainder of 1.
%e A375117 Row(4) is {1, 3}, because 2^4-1 = 16-1 = 15, and 15 divided by 4 leaves a remainder of 3, and 4 divided by 3 leaves a remainder of 1.
%o A375117 (PARI) row(n) = my(x=2^n-1, y=n, ok=1, list=List()); while (ok, my(z=divrem(x, y)); x = y; y = z[2]; if (y==0, ok=0, listput(list, y));); listsort(list); Vec(list); \\ _Michel Marcus_, Jul 31 2024
%Y A375117 Cf. A049816, A014491.
%K A375117 nonn,tabf
%O A375117 2,4
%A A375117 _Mike Jones_, Jul 30 2024
%E A375117 More terms from _Michel Marcus_, Jul 31 2024