OFFSET
1,3
COMMENTS
n is in this sequence iff it occurs in one of A002283, A007185, A016090, A198971, A199685, A216092, A216093, A224473, A224474, A224475, A224476, A224477, and A224478. - Eric M. Schmidt, Apr 08 2013
Let q(n) = floor(a(n)^3 / 10^A055642(a(n))), where A055642(n) is the number of digits in the decimal expansion of n. As well, let na and nb denote the indices of the preceding and next terms that begin with a 9. Then (1/q(n)) * (a(n)^4 - a(n)^3 - a(n)^2 + a(n)) - 2*a(n)^2 + a(n) + q(n) + 1 = a(na+nb-n)^2 - a(na+nb-n) - q(na+nb-n). - Christopher Hohl, Apr 08 2019
REFERENCES
S. Premchaud, A class of numbers, Math. Student, 48 (1980), 293-300.
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Robert Dawson, On Some Sequences Related to Sums of Powers, J. Int. Seq., Vol. 21 (2018), Article 18.7.6.
Eric Weisstein's World of Mathematics, Trimorphic Number
EXAMPLE
376^3 = 53157376 which ends with 376.
MATHEMATICA
Do[x=Floor[N[Log[10, n], 25]]+1; If[Mod[n^3, 10^x] == n, Print[n]], {n, 1, 10000}]
Select[Range[100000], PowerMod[#, 3, 10^IntegerLength[#]]==#&](* Harvey P. Dale, Nov 04 2011 *)
Select[Range[0, 10^5], 10^IntegerExponent[#^3-#, 10]>#&] (* Jean-François Alcover, Apr 04 2013 *)
PROG
(Magma) [n: n in [0..10^5] | Intseq(n^3)[1..#Intseq(n)] eq Intseq(n)]; // Bruno Berselli, Apr 04 2013
CROSSREFS
KEYWORD
base,nonn
AUTHOR
STATUS
approved