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%I #12 Nov 13 2017 22:05:41
%S 7,68,70,324,680,700,3240,6800,7000,7618,31177,32400,52308,68000,
%T 69314,70000,76180,311770,324000,353068,523080,680000,693140,700000,
%U 756658,761800,1039247,2715974,2732441,3117700,3240000,3511617,3530680,4689368,5230800,6800000,6931400,7000000
%N Numbers n such that the largest digit of n^3 is 4.
%C For any term a(n), all numbers of the form a(n)*10^k, k >= 0, are in this sequence. Primitive terms, i.e., not of this form (or equivalently: without trailing '0'), are 7, 68, 324, 7618, 31177, 52308, 69314, 353068, 756658, 1039247, 2715974, 2732441, 3511617, 4689368, 7571814, 12811968, 15904541, ...
%C All terms have last nonzero digit 1, 4, 7 or 8 and leading digit <= 7. - _Robert Israel_, Nov 13 2017
%C The number formed by the first m digits of a term is always less than c*10^m with c = (4/9)^(1/3) = .7631428283688879... - _M. F. Hasler_, Nov 13 2017
%e 7 is in the sequence because the largest digit of 7^3 = 343 is 4.
%p select(n -> max(convert(n^3,base,10))=4, [$1..10^6]); # _Robert Israel_, Nov 13 2017
%o (PARI) for(n=1,2e8, vecmax(digits(n^3))==4&&print1(n","))
%Y Cf. A294663 (the corresponding cubes), A278937, A294665, A294996 - A294999 (analog for digits 3, 5, 6 - 9); A277961 (analog for squares).
%Y Cf. A000578 (the cubes).
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Nov 12 2017