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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.
1
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).
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
Sequence in context: A106486 A195743 A106494 * A339811 A015135 A116619
KEYWORD
nonn,base,tabf
AUTHOR
Rémy Sigrist, Aug 12 2022
STATUS
approved