A321281 a(n) is the number of primes of the form p*10^n + q, where p, q are the digits from 1 to 9.

21, 15, 13, 8, 9, 5, 3, 8, 8, 2, 2, 3, 2, 0, 2, 2, 2, 3, 2, 5, 1, 4, 0, 3, 1, 1, 1, 2, 2, 0, 2, 0, 0, 0, 2, 2, 1, 1, 3, 1, 0, 2, 0, 0, 3, 2, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 2, 1, 0, 2, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1

Offset: 1

Author

Anton Deynega, Nov 10 2018

Keywords

• nonn
• base

Examples

			a(6) = 5 because there are five primes of the form p*10^6 + q where p, q are the digits from 1 to 9: 1000003, 2000003, 7000003, 7000009, 8000009.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3000
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Crossrefs

Cf. A000040.

Programs

Maple

f:= n -> nops(select(isprime,[seq(seq(p*10^n+q,p=1..9),q=[1,3,7, 9])])):
map(f, [$1..100]); # Robert Israel, Nov 14 2018

Mathematica

a[n_]:=(c=0; Do[ Do[ If[PrimeQ[i*10^n+j], c++], {i,1,9}], {j,1,9,2}]; c); Array[a, 20] (* Amiram Eldar, Nov 14 2018 *)

PARI

a(n)={my(t=10^n); sum(i=1, 9, sum(j=1, 5, isprime(2*j-1+i*t)))} \\ Andrew Howroyd, Nov 10 2018

Extensions

a(16)-a(86) from Andrew Howroyd, Nov 10 2018