A301943 Number of primes of the form b^2+1 for b <= 10^n that end in 1.

1, 4, 42, 279, 2236, 18155, 152020, 1317648, 11634451, 104116591, 942191087

Offset

1,2

Links

Table of n, a(n) for n=1..11.

Formula

a(n) + A301944(n) + 2 = A206709(n).

Example

101, 401, 1601 and 8101 are primes; so a(2) = 4.

Mathematica

c = k = 0; lst = {}; Do[ While[k <= 10^n, If[ PrimeQ[k^2 + 1], c++]; k+=10]; AppendTo[lst, c]; Print[c], {n, 9}] (* Robert G. Wilson v, Mar 30 2018 *)

Prog

(Python)
from sympy import isprime
def A301943(n):
    return sum(1 for i in range(1, 10**(n-1)+1) if isprime(100*i**2+1)) # Chai Wah Wu, Mar 30 2018

Crossrefs

Cf. A002496, A206709, A301944.

Sequence in context: A220835 A157719 A280956 * A219101 A118447 A219980

Adjacent sequences: A301940 A301941 A301942 * A301944 A301945 A301946

Keyword

nonn,more,base

Author

Seiichi Manyama, Mar 29 2018

Extensions

a(10) from Robert G. Wilson v, Mar 31 2018

a(11) from Robert G. Wilson v, Apr 04 2018

Status

approved