

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.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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 presentday mathematics.  N. J. A. Sloane, Mar 03 2018]


LINKS

Table of n, a(n) for n=1..69.


EXAMPLE

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


MATHEMATICA

p[n_] := Module[{k = 1}, While[Union[PrimeQ /@ IntegerDigits[n*Prime[k]]] != {True}, k++]; Prime[k]]; p /@ Prime[Range[100]]


PROG

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


CROSSREFS

Cf. A046034.
Sequence in context: A061186 A135684 A220295 * A321108 A126610 A087380
Adjacent sequences: A300286 A300287 A300288 * A300290 A300291 A300292


KEYWORD

nonn,base


AUTHOR

Ivan N. Ianakiev, Mar 02 2018


EXTENSIONS

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


STATUS

approved



