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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
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
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Aug 28 2012
EXTENSIONS
a(17)-a(31) from Donovan Johnson, Aug 28 2012
STATUS
approved