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.

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, 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, 11, 13, 15, 16, 2, 3, 4, 5, 7, 8, 9, 13, 15, 16, 17, 17, 18

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..79.

Formula

T(n, 1) = A356552(n).

T(n, A080221(n)-1) = n for n > 1.

T(n, A080221(n)) = n+1.

Example

Triangle T(n, k) begins:
    n    n-th row
    --   --------
     1   [2]
     2   [2, 3]
     3   [3, 4]
     4   [2, 3, 4, 5]
     5   [5, 6]
     6   [2, 3, 4, 5, 6, 7]
     7   [7, 8]
     8   [2, 3, 4, 5, 7, 8, 9]
     9   [3, 4, 7, 9, 10]
    10   [2, 3, 5, 6, 9, 10, 11]
    11   [11, 12]
    12   [2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13]
    13   [13, 14]
    14   [7, 8, 13, 14, 15]
    15   [3, 5, 6, 7, 11, 13, 15, 16]
    16   [2, 3, 4, 5, 7, 8, 9, 13, 15, 16, 17]
    17   [17, 18]

Prog

(PARI) row(n) = select(b -> n % sumdigits(n, b)==0, [2..n+1])
(Python)
from sympy.ntheory import digits
def row(n): return [b for b in range(2, n+2) if n%sum(digits(n, b)[1:])==0]
print([an for n in range(1, 18) for an in row(n)]) # Michael S. Branicky, Aug 12 2022

Crossrefs

Cf. A080221, A356552.

Sequence in context: A106486 A195743 A106494 * A339811 A015135 A116619

Adjacent sequences: A356552 A356553 A356554 * A356556 A356557 A356558

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Aug 12 2022

Status

approved