cp's OEIS Frontend

A356555 Irregular triangle T(n, k), n > 0, k = 1..A080221(n) read by rows; the n-th row contains, in ascending order, the bases b from 2..n+1 where the sum of digits of n divides n.

%I A356555 #10 Aug 15 2022 05:22:59
%S A356555 2,2,3,3,4,2,3,4,5,5,6,2,3,4,5,6,7,7,8,2,3,4,5,7,8,9,3,4,7,9,10,2,3,5,
%T A356555 6,9,10,11,11,12,2,3,4,5,6,7,9,10,11,12,13,13,14,7,8,13,14,15,3,5,6,7,
%U A356555 11,13,15,16,2,3,4,5,7,8,9,13,15,16,17,17,18
%N A356555 Irregular triangle T(n, k), n > 0, k = 1..A080221(n) read by rows; the n-th row contains, in ascending order, the bases b from 2..n+1 where the sum of digits of n divides n.
%C A356555 A080221 provides row lengths (note that for n > 0, we consider the base n+1 but not the base 1, unlike A080221 that considers the base 1 but not the base n+1, however this does not matter as the sums of digits of n in base 1 and base n+1 are the same).
%F A356555 T(n, 1) = A356552(n).
%F A356555 T(n, A080221(n)-1) = n for n > 1.
%F A356555 T(n, A080221(n)) = n+1.
%e A356555 Triangle T(n, k) begins:
%e A356555     n    n-th row
%e A356555     --   --------
%e A356555      1   [2]
%e A356555      2   [2, 3]
%e A356555      3   [3, 4]
%e A356555      4   [2, 3, 4, 5]
%e A356555      5   [5, 6]
%e A356555      6   [2, 3, 4, 5, 6, 7]
%e A356555      7   [7, 8]
%e A356555      8   [2, 3, 4, 5, 7, 8, 9]
%e A356555      9   [3, 4, 7, 9, 10]
%e A356555     10   [2, 3, 5, 6, 9, 10, 11]
%e A356555     11   [11, 12]
%e A356555     12   [2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13]
%e A356555     13   [13, 14]
%e A356555     14   [7, 8, 13, 14, 15]
%e A356555     15   [3, 5, 6, 7, 11, 13, 15, 16]
%e A356555     16   [2, 3, 4, 5, 7, 8, 9, 13, 15, 16, 17]
%e A356555     17   [17, 18]
%o A356555 (PARI) row(n) = select(b -> n % sumdigits(n,b)==0, [2..n+1])
%o A356555 (Python)
%o A356555 from sympy.ntheory import digits
%o A356555 def row(n): return [b for b in range(2, n+2) if n%sum(digits(n, b)[1:])==0]
%o A356555 print([an for n in range(1, 18) for an in row(n)]) # _Michael S. Branicky_, Aug 12 2022
%Y A356555 Cf. A080221, A356552.
%K A356555 nonn,base,tabf
%O A356555 1,1
%A A356555 _Rémy Sigrist_, Aug 12 2022