This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A033819 #80 Mar 14 2025 20:02:51
%S A033819 0,1,4,5,6,9,24,25,49,51,75,76,99,125,249,251,375,376,499,501,624,625,
%T A033819 749,751,875,999,1249,3751,4375,4999,5001,5625,6249,8751,9375,9376,
%U A033819 9999,18751,31249,40625,49999,50001,59375,68751,81249,90624,90625
%N 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).
%C A033819 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
%C A033819 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
%D A033819 S. Premchaud, A class of numbers, Math. Student, 48 (1980), 293-300.
%H A033819 Eric M. Schmidt, <a href="/A033819/b033819.txt">Table of n, a(n) for n = 1..1000</a>
%H A033819 Robert Dawson, <a href="https://www.emis.de/journals/JIS/VOL21/Dawson/dawson6.html">On Some Sequences Related to Sums of Powers</a>, J. Int. Seq., Vol. 21 (2018), Article 18.7.6.
%H A033819 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_2">Elegance of Squares, Cubes, and Higher Powers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 2, 29-81.
%H A033819 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TrimorphicNumber.html">Trimorphic Number</a>
%H A033819 <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>
%e A033819 376^3 = 53157376 which ends with 376.
%t A033819 Do[x=Floor[N[Log[10, n], 25]]+1; If[Mod[n^3, 10^x] == n, Print[n]], {n, 1, 10000}]
%t A033819 Select[Range[100000],PowerMod[#,3,10^IntegerLength[#]]==#&](* _Harvey P. Dale_, Nov 04 2011 *)
%t A033819 Select[Range[0, 10^5], 10^IntegerExponent[#^3-#, 10]>#&] (* _Jean-François Alcover_, Apr 04 2013 *)
%o A033819 (Magma) [n: n in [0..10^5] | Intseq(n^3)[1..#Intseq(n)] eq Intseq(n)]; // _Bruno Berselli_, Apr 04 2013
%Y A033819 Cf. A074194, A215558 (cubes of the terms).
%K A033819 base,nonn
%O A033819 1,3
%A A033819 _David W. Wilson_