A301943 - OEIS

%I #34 Apr 04 2018 10:05:29

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

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

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

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

%t 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 *)

%o (Python)

%o from sympy import isprime

%o def A301943(n):

%o     return sum(1 for i in range(1,10**(n-1)+1) if isprime(100*i**2+1)) # _Chai Wah Wu_, Mar 30 2018

%Y Cf. A002496, A206709, A301944.

%K nonn,more,base

%O 1,2

%A _Seiichi Manyama_, Mar 29 2018

%E a(10) from _Robert G. Wilson v_, Mar 31 2018

%E a(11) from _Robert G. Wilson v_, Apr 04 2018