A271637 Squared-squares in base 2: numbers n such that n^2 in base 2 is of the form xx for a string x.

6, 820, 104391567, 119304648, 858993460, 900719925474100, 26202761468337432, 29478106651879611, 32753451835421790, 225701339254799219773, 243062980735937621294, 260424622217076022815, 277786263698214424336, 944473296573929042740, 232485734541274841289650

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

The base-2 analog of A106497.

Sequence in context: A365511 A321426 A281566 * A249126 A337162 A281690

Adjacent sequences: A271634 A271635 A271636 * A271638 A271639 A271640

Keyword

nonn

Author

Jeffrey Shallit, Apr 11 2016

Extensions

a(7)-a(15) from Giovanni Resta, Apr 11 2016

Status

approved