A215952 Numbers n such that n^2 written in base 10 is of the form xyx where x is any string of digits and y is any single digit.

1, 2, 3, 11, 22, 26, 173, 212, 263, 276, 16262, 27073, 193744, 208139, 311207, 2445865, 112791955, 142048458, 142837143, 153856154, 161933320, 164855165, 181838182, 200085674, 203701046, 213072687, 224870383, 225583910, 244765245, 252717253, 265704266

Offset

1,2

Comments

J. Brennen found the (prime) term 252717253.

Links

Jack Brennen, Table of n, a(n) for n = 1..66

Woodhodgson, Digit block repetition in prime squares, Yahoo! group primenumbers, Aug 28 2012.

Woodhodgson, Jack Brennen, Maximilian Hasler, Digit block repetition in prime squares, digest of 7 messages in primenumbers Yahoo group, Aug 28 - Aug 30, 2012.

Example

The squares of n=1,2,3 are < 10 and thus of the form xyx, where x is an empty string.
a(4) = 11 since 11^2 = 121 = xyx  with  x=1 and y=2.
a(7) = 173 since 173^2 = 29929 = xyx with x=29 and y=9.

Prog

(PARI) {t=1; m=3; for(n=1, 1e9, n>m & (m=sqrt((n=t*=10)^2*10)) & next; [.1, -1]*divrem(n^2, t)\1 || print1(n", "))}

Crossrefs

Sequence in context: A002778 A028816 A316187 * A276375 A128921 A118595

Adjacent sequences: A215949 A215950 A215951 * A215953 A215954 A215955

Keyword

nonn,base

Author

M. F. Hasler, Aug 28 2012

Extensions

a(17)-a(31) from Donovan Johnson, Aug 28 2012

Status

approved