login
A338129
Positive numbers k such that the binary representation of k^k ends with that of k.
2
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.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 11 2020
STATUS
approved