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%I #31 Oct 20 2023 06:44:42
%S 1,7,19,67,124499,594959999,1349969999,57999659949,84936699999,
%T 498998999999
%N 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).
%C I've also found 498998999999, 7494994999999, 34999974999999 and some larger numbers, but not all values in between have been checked.
%C 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.
%C Is this sequence finite? - _Charles R Greathouse IV_, Jan 12 2012
%C 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
%C a(11) > 10^12. - _Delbert L. Johnson_, May 01 2023
%F A122484 = { k in A067251 | A007953(k) >= A007953(k^4) }. - _M. F. Hasler_, Jan 14 2012
%e 67 is a term because 67 has a digital sum of 13 and 67^4 = 20151121 which also has a digital sum of 13.
%e 594959999 has a digital sum of 68 and 594959999^4 has a digital sum of 67, i.e., less than 68.
%o (PARI) is_A122484(n)= n%10 && A007953(n) >= A007953(n^4) \\ _M. F. Hasler_, Jan 14 2012
%Y Cf. A064210.
%K base,nonn,more
%O 1,2
%A _Martin Raab_, Sep 15 2006
%E a(8) and a(9) from _Martin Raab_, Oct 17 2008
%E a(10) from _Delbert L. Johnson_, May 01 2023
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