A131581 The next prime greater than the square root of 10^n.

2, 5, 11, 37, 101, 317, 1009, 3163, 10007, 31627, 100003, 316241, 1000003, 3162283, 10000019, 31622777, 100000007, 316227767, 1000000007, 3162277669, 10000000019, 31622776621, 100000000003, 316227766069, 1000000000039

Offset: 0

Author

Robert G. Wilson v, Jan 12 2007

Keywords

• easy
• nonn

Comments

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, ....

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.

Crossrefs

Cf. A003617, A132153, A136582, A175733, A175734.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Table[ NextPrim@ Floor@ Sqrt[10^n], {n, 0, 25}]
Table[NextPrime[Sqrt[10^n]],{n,0,30}] (* Harvey P. Dale, Aug 15 2017 *)

Formula

a(n) = sqrt(A175733(n+1)). [From Jaroslav Krizek, Aug 24 2010]