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A233453
Numbers k such that k^7 starts with k itself (in base 10).
7
0, 1, 10, 100, 1000, 6813, 10000, 14678, 46416, 100000, 146780, 464159, 1000000, 4641589, 10000000, 21544347, 68129207, 100000000, 1000000000, 10000000000, 100000000000, 316227766017, 681292069058, 1000000000000, 2154434690032, 10000000000000, 21544346900319
OFFSET
1,3
EXAMPLE
6813^7 = 681347587591081074493576917 begins with 6813, so 6813 is in the sequence.
MATHEMATICA
Join[{0}, Select[Range[0, 5*10^6], IntegerDigits[#]==Take[IntegerDigits[ #^7], IntegerLength[ #]]&]] (* The program generates the first 14 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Mar 31 2022 *)
PROG
(PARI) r=80; print1(1, ", "); e=7; for(n=2, r, p=round((10^(1/(e-1)))^n); f=p^e; b=10^(#Str(f)-#Str(p)); if((f-lift(Mod(f, b)))/b==p, print1(p, ", ")));
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
0 inserted by Juhani Heino, Aug 31 2015
STATUS
approved