A338129 Positive numbers k such that the binary representation of k^k ends with that of k.

1, 3, 5, 7, 9, 13, 15, 17, 25, 31, 33, 41, 49, 57, 63, 65, 81, 97, 113, 127, 129, 145, 161, 177, 193, 209, 225, 241, 255, 257, 289, 321, 353, 385, 417, 449, 481, 511, 513, 545, 577, 609, 641, 673, 705, 737, 769, 801, 833, 865, 897, 929, 961, 993, 1023, 1025

Offset

1,2

Comments

This sequence is infinite as it contains the positive terms of A000225.

All terms are odd.

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, Binary plot of the terms < 2^16

Index entries for sequences related to automorphic numbers

Example

The binary representation of 3^3 ("11011") ends with that of 3 ("11"), so 3 is a term.

Mathematica

Select[Range[1200], Take[IntegerDigits[#^#, 2], -IntegerLength[ #, 2]] == IntegerDigits[ #, 2]&] (* Harvey P. Dale, Jan 12 2022 *)

Prog

(PARI) is(n, base=2) = Mod(n, base^#digits(n, base))^n==n

Crossrefs

Cf. A000225, A082576, A338128, A338130.

Sequence in context: A003532 A156982 A224195 * A327573 A306069 A270807

Adjacent sequences: A338126 A338127 A338128 * A338130 A338131 A338132

Keyword

nonn,base

Author

Rémy Sigrist, Oct 11 2020

Status

approved