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%I #24 Aug 08 2014 01:23:17
%S 2,5,11,37,107,337,1061,3343,10559,33343,105517,333337,1054133,
%T 3333373,10540931,33333359,105409309,333333361,1054092869,3333333413,
%U 10540925639,33333333343,105409255363,333333333367,1054092553583,3333333333383,10540925534207
%N Least prime such that p^2 is a zeroless n-digit number.
%H M. F. Hasler, <a href="/A195985/b195985.txt">Table of n, a(n) for n = 1..158</a>
%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_607.htm">Puzzle 607. A zeroless Prime power</a>, on primepuzzles.net, Sept. 24, 2011.
%H W. Schneider, <a href="http://oeis.org/A007496/a007496.html">NoZeros: Powers n^k without Digit Zero</a> (local copy of www.wschnei.de/digit-related-numbers/nozeros.html), as of Jan 30 2003.
%e a(1)^2=4, a(2)^2=25, a(3)^2=121, a(4)^2=1369 are the least squares of primes with 1, 2, 3 resp. 4 digits, and these digits are all nonzero.
%e a(5)=107 since 101^2=10201 and 103^2=10609 both contain a zero digit, but 107^2=11449 does not.
%e a(1000)=[10^500/3]+10210 (500 digits), since primes below sqrt(10^999) = 10^499*sqrt(10) ~ 3.162e499 have squares of less than 1000 digits, between sqrt(10^999) and 10^500/3 = sqrt(10^1000/9) ~ 3.333...e499 they have at least one zero digit. Finally, the 7 primes between 10^500/3 and a(1000) also happen to have a "0" digit in their square, but not so
%e a(1000)^2 = 11111...11111791755555...55555659792849
%e = [10^500/9]*(10^500+5) + 6806*10^500+104237294.
%o (PARI) a(n)={ my(p=sqrtint(10^n\9)-1); until( is_A052382(p^2), p=nextprime(p+2));p}
%Y Cf. A195942, A195943, A195944, A195945, A195946, A195908, A195948, A007377, A008839, A030700, A030701, A030702, A030703, A030704, A030705, A030706.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Sep 26 2011
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