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A122484
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Numbers k not ending in zero such that the sum of digits of k is >= the sum of digits of k^4 (in base 10).
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4
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OFFSET
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1,2
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COMMENTS
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I've also found 498998999999, 7494994999999, 34999974999999 and some larger numbers, but not all values in between have been checked.
One is likely to find an example of the form 5*10^j - m*10^floor(j/2) - 1 or 7.5*10^j - m*10^floor(j/2) - 1 for j > 12 within the first 10^(floor(j/2)-1) m's.
This sequence is infinite: for N = 7.5*10^j - 40*10^floor(j/2) - 1 one has A007953(N) = 9j-2 and A007953(N^4) <= 9j-2 for all j > 16, with equality for all even j > 16. - M. F. Hasler, Jan 14 2012
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LINKS
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FORMULA
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EXAMPLE
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67 is a term because 67 has a digital sum of 13 and 67^4 = 20151121 which also has a digital sum of 13.
594959999 has a digital sum of 68 and 594959999^4 has a digital sum of 67, i.e., less than 68.
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PROG
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CROSSREFS
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KEYWORD
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base,nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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