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 A033819 Trimorphic numbers: n^3 ends with n. Also m-morphic numbers for all m > 5 such that m-1 is not divisible by 10 and m == 3 (mod 4). 29
 0, 1, 4, 5, 6, 9, 24, 25, 49, 51, 75, 76, 99, 125, 249, 251, 375, 376, 499, 501, 624, 625, 749, 751, 875, 999, 1249, 3751, 4375, 4999, 5001, 5625, 6249, 8751, 9375, 9376, 9999, 18751, 31249, 40625, 49999, 50001, 59375, 68751, 81249, 90624, 90625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(1) through a(13) are the rightmost digit or pair of digits in A215558. - Jonathan Vos Post, Aug 16 2012 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. MAPLE P:=proc(n) if n^3 mod 10^(ilog10(n)+1)=n then n; fi; end: seq(P(i), i=0..90625); # Paolo P. Lava, Jun 25 2018 MATHEMATICA Do[x=Floor[N[Log[10, n], 25]]+1; If[Mod[n^3, 10^x] == n, Print[n]], {n, 1, 10000}] Select[Range, 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 Cf. A074194, A215558. Sequence in context: A091730 A058076 A238712 * A058782 A115762 A169889 Adjacent sequences:  A033816 A033817 A033818 * A033820 A033821 A033822 KEYWORD base,nonn AUTHOR STATUS approved

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Last modified October 20 08:05 EDT 2019. Contains 328252 sequences. (Running on oeis4.)