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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..3000

Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000040.

Sequence in context: A068015 A040422 A214037 * A048933 A142590 A346064

Adjacent sequences: A321278 A321279 A321280 * A321282 A321283 A321284

Keyword

nonn,base

Author

Anton Deynega, Nov 10 2018

Extensions

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

Status

approved