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A338130
Positive numbers k such that the ternary representation of k^k ends with that of k.
2
1, 4, 7, 10, 19, 28, 37, 46, 55, 64, 73, 82, 109, 136, 163, 190, 217, 244, 271, 298, 325, 352, 379, 406, 433, 460, 487, 514, 541, 568, 595, 622, 649, 676, 703, 730, 811, 892, 973, 1054, 1135, 1216, 1297, 1378, 1459, 1540, 1621, 1702, 1783, 1864, 1945, 2026
OFFSET
1,2
COMMENTS
All terms are of the form 3*m + 1 for some m >= 0.
The first differences appear to contain only powers of 3 and to be weakly increasing.
Run lengths in first differences appear to be regular and suggest a simple procedure to generate the sequence.
LINKS
Rémy Sigrist, Ternary plot of the terms < 3^10 (blue squares correspond to 1's and red squares to 2's)
EXAMPLE
The ternary representation of 4^4 ("100111") ends with that of 4 ("11"), so 4 is a term.
MATHEMATICA
Select[Range[2100], Take[IntegerDigits[#^#, 3], -IntegerLength[#, 3]] == IntegerDigits[ #, 3]&] (* Harvey P. Dale, Feb 13 2022 *)
PROG
(PARI) is(n, base=3) = Mod(n, base^#digits(n, base))^n==n
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 11 2020
STATUS
approved