OFFSET
1,1
COMMENTS
The base-2 expansion must be canonical (not start with leading zeros).
The sequence is infinite, as (4/5)*(2^(20*k + 10) + 1) has the property for k >= 0.
REFERENCES
Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations, Experimental Math, 28 (2019), 428-439.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..398(terms < 2^270)
Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations, arXiv:1707.03894 [math.NT], 2017. See p. 10.
EXAMPLE
The number 6 is in the sequence because 36 = 6^2 and 36 in base 2 is 100100, which is xx for x = 100.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Apr 11 2016
EXTENSIONS
a(7)-a(15) from Giovanni Resta, Apr 11 2016
STATUS
approved