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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). 25
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

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

Eric Weisstein's World of Mathematics, Trimorphic Number

Index entries for sequences related to automorphic numbers

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-Fran├žois 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

David W. Wilson

STATUS

approved

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Last modified June 22 14:21 EDT 2017. Contains 288632 sequences.