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%I #28 Nov 12 2019 15:05:25
%S 1,2,3,11,22,26,173,212,263,276,16262,27073,193744,208139,311207,
%T 2445865,112791955,142048458,142837143,153856154,161933320,164855165,
%U 181838182,200085674,203701046,213072687,224870383,225583910,244765245,252717253,265704266
%N 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.
%C J. Brennen found the (prime) term 252717253.
%H Jack Brennen, <a href="/A215952/b215952.txt">Table of n, a(n) for n = 1..66</a>
%H Woodhodgson, <a href="http://groups.yahoo.com/group/primenumbers/message/24405">Digit block repetition in prime squares</a>, Yahoo! group primenumbers, Aug 28 2012.
%H Woodhodgson, Jack Brennen, Maximilian Hasler, <a href="/A215952/a215952.txt">Digit block repetition in prime squares</a>, digest of 7 messages in primenumbers Yahoo group, Aug 28 - Aug 30, 2012.
%e The squares of n=1,2,3 are < 10 and thus of the form xyx, where x is an empty string.
%e a(4) = 11 since 11^2 = 121 = xyx with x=1 and y=2.
%e a(7) = 173 since 173^2 = 29929 = xyx with x=29 and y=9.
%o (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","))}
%K nonn,base
%O 1,2
%A _M. F. Hasler_, Aug 28 2012
%E a(17)-a(31) from _Donovan Johnson_, Aug 28 2012
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