A338129 -id:A338129 - cp's OEIS frontend

A338130 Positive numbers k such that the ternary representation of k^k ends with that of k.

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

Rémy Sigrist, Oct 11 2020

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.

			The ternary representation of 4^4 ("100111") ends with that of 4 ("11"), so 4 is a term.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Ternary plot of the terms < 3^10 (blue squares correspond to 1's and red squares to 2's)
Index entries for sequences related to automorphic numbers

Cf. A082576, A338128, A338129.

Select[Range[2100],Take[IntegerDigits[#^#,3],-IntegerLength[#,3]] == IntegerDigits[ #,3]&] (* Harvey P. Dale, Feb 13 2022 *)

is(n, base=3) = Mod(n, base^#digits(n, base))^n==n

cp's OEIS Frontend

A338130 Positive numbers k such that the ternary representation of k^k ends with that of k.

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