A300289 a(n) is the smallest prime p such that the product of p and prime(n) contains only prime digits, or -1 if no such prime p exists.

11, 11, 5, 5, 2, 29, 19, 3, 11, 13, 17, 61, 13, 59, 5, 61, 43, 37, 5, 5, 101, 3, 31, 307, 59, 23, 541, 5, 3, 29, 179, 17, 1721, 257, 17, 5, 239, 229, 199, 149, 3, 13, 3, 1439, 281, 127, 107, 101, 9791, 163, 31, 107, 3, 3, 139, 199, 83, 13, 929, 83, 19, 11, 11, 107, 71, 181, 167, 661, 1031

Offset: 1

Author

Ivan N. Ianakiev, Mar 02 2018

Keywords

• nonn
• base

Comments

If a(i) = prime(j), then a(j) <= prime(i). - Rémy Sigrist, Mar 03 2018. [Note that this does not imply that a prime p always exists! In fact if r and s are large primes, r*s will surely contain a nonprime digit, although this kind of question is beyond the reach of present-day mathematics. - N. J. A. Sloane, Mar 03 2018]

Examples

			11 is the smallest prime such that 11*prime(1)=22 consists of only prime digits. Therefore a(1) = 11.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A046034.

Programs

Mathematica

p[n_] := Module[{k = 1},  While[Union[PrimeQ /@ IntegerDigits[n*Prime[k]]] != {True}, k++]; Prime[k]]; p /@ Prime[Range[100]]
spp[p_]:=Module[{k=2},While[AnyTrue[IntegerDigits[p*k],!PrimeQ[#]&],k=NextPrime[k]];k]; Table[spp[p],{p,Prime[Range[70]]}] (* Harvey P. Dale, Jun 20 2023 *)

PARI

a(n) = {forprime(p=2, , if (#select(x->(! isprime(x)), digits(p*prime(n))) == 0, return (p)););} \\ Michel Marcus, Mar 02 2018

Extensions

Escape clause added to definition by N. J. A. Sloane, Mar 03 2018