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A152147
Irregular triangle in which row n lists k > 0 such that the sum of digits of k^n equals k.
14
1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 9, 1, 8, 17, 18, 26, 27, 1, 7, 22, 25, 28, 36, 1, 28, 35, 36, 46, 1, 18, 45, 54, 64, 1, 18, 27, 31, 34, 43, 53, 58, 68, 1, 46, 54, 63, 1, 54, 71, 81, 1, 82, 85, 94, 97, 106, 117, 1, 98, 107, 108, 1, 108, 1, 20, 40, 86, 103, 104, 106, 107, 126, 134, 135
OFFSET
1,2
COMMENTS
Each row begins with 1 and has length A046019(n).
EXAMPLE
1, 2, 3, 4, 5, 6, 7, 8, 9;
1, 9;
1, 8, 17, 18, 26, 27; (A046459, with 0)
1, 7, 22, 25, 28, 36; (A055575 " )
1, 28, 35, 36, 46; (A055576 " )
1, 18, 45, 54, 64; (A055577 " )
1, 18, 27, 31, 34, 43, 53, 58, 68; (A226971 " )
1, 46, 54, 63;
1, 54, 71, 81,
1, 82, 85, 94, 97, 106, 117,
1, 98, 107, 108, etc.
PROG
(Python)
def ok(k, r): return sum(map(int, str(k**r))) == k
def agen(rows, startrow=1, withzero=0):
for r in range(startrow, rows + startrow):
d, lim = 1, 1
while lim < r*9*d: d, lim = d+1, lim*10
yield from [k for k in range(1-withzero, lim+1) if ok(k, r)]
print([an for an in agen(13)]) # Michael S. Branicky, May 23 2021
CROSSREFS
KEYWORD
base,tabf,nonn
AUTHOR
T. D. Noe, Nov 26 2008
STATUS
approved