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

1,2

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, 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

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

Cf. A082576, A338128, A338129.

Sequence in context: A027752 A161334 A111981 * A373655 A080922 A227686

Adjacent sequences: A338127 A338128 A338129 * A338131 A338132 A338133

Keyword

nonn,base

Author

Rémy Sigrist, Oct 11 2020

Status

approved