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A152147
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Irregular triangle in which row n lists k > 0 such that the sum of digits of k^n equals k.
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13
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Each row begins with 1 and has length A046019(n).
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LINKS
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EXAMPLE
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1, 2, 3, 4, 5, 6, 7, 8, 9;
1, 9;
1, 8, 17, 18, 26, 27; (A046459, with 0)
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.
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PROG
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(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)]
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CROSSREFS
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KEYWORD
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base,tabf,nonn
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AUTHOR
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STATUS
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approved
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