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%I #11 Aug 15 2017 17:14:28
%S 2,5,11,37,101,317,1009,3163,10007,31627,100003,316241,1000003,
%T 3162283,10000019,31622777,100000007,316227767,1000000007,3162277669,
%U 10000000019,31622776621,100000000003,316227766069,1000000000039
%N The next prime greater than the square root of 10^n.
%C The difference between a(n) and floor(sqrt(10^n)): 1, 2, 1, 6, 1, 1, 9, 1, 7, 5, 3, 14, 3, 6, 19, 1, 7, 1, 7, 9, ....
%C Values for which the difference between a(n) and floor(sqrt(10^n)) equals one: 0, 2, 4, 5, 7, 15, 17, 25, 145, 1079, ..., (1350). Only even terms are 0, 2 & 4; all the rest must be odd.
%F a(n) = sqrt(A175733(n+1)). [From _Jaroslav Krizek_, Aug 24 2010]
%t NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Table[ NextPrim@ Floor@ Sqrt[10^n], {n, 0, 25}]
%t Table[NextPrime[Sqrt[10^n]],{n,0,30}] (* _Harvey P. Dale_, Aug 15 2017 *)
%Y Cf. A003617, A132153, A136582, A175733, A175734.
%K easy,nonn
%O 0,1
%A _Robert G. Wilson v_, Jan 12 2007
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