A135944 Number of n-digit primes whose digits are all primes.

4, 4, 15, 38, 128, 389, 1325, 4643, 16623, 59241, 214432, 781471, 2884201, 10687480, 39838489, 149172297, 560795383, 2115430020

Offset

1,1

Comments

Number of primes of the form: ...d3d2d1d0 = d0 * 10 ^ 0 + d1 * 10 ^ 1 + d2 * 10 ^ 2 + d3 * 10 ^ 3 + ... where d0, d1, d2, d3, ... are primes with one digit. The i-th element of the sequence is the number of primes with i digits. Approximation of the sum of the sequence up to a(k) for large values of k: Sum_{i=1..k} a(i) = 10^k / (k*log(10))*(2/5)^(k-1).

Links

Table of n, a(n) for n=1..18.

Example

a(4) = 38 because there are 38 numbers of the form d3d2d1d0 with d0, d1, d2, d3 prime numbers, namely, 2237, 2273, 2333, 2357, 2377, 2557, ..., 7753, 7757.

Crossrefs

Cf. A135945, A135946.

Sequence in context: A198313 A219350 A222511 * A268169 A177241 A076821

Adjacent sequences: A135941 A135942 A135943 * A135945 A135946 A135947

Keyword

nonn,base,more

Author

Giorgio Balzarotti & Paolo P. Lava, Dec 07 2007

Extensions

a(12)-a(14) from Donovan Johnson, Feb 05 2010

a(15)-a(16) from Chai Wah Wu, Nov 28 2015

a(17)-a(18) from Giovanni Resta, May 25 2016

Status

approved