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A300289
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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]
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LINKS
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Table of n, a(n) for n=1..69.
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EXAMPLE
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11 is the smallest prime such that 11*prime(1)=22 consists of only prime digits. Therefore a(1) = 11.
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MATHEMATICA
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p[n_] := Module[{k = 1}, While[Union[PrimeQ /@ IntegerDigits[n*Prime[k]]] != {True}, k++]; Prime[k]]; p /@ Prime[Range[100]]
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PROG
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(PARI) a(n) = {forprime(p=2, , if (#select(x->(! isprime(x)), digits(p*prime(n))) == 0, return (p)); ); } \\ Michel Marcus, Mar 02 2018
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CROSSREFS
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Cf. A046034.
Sequence in context: A061186 A135684 A220295 * A321108 A126610 A087380
Adjacent sequences: A300286 A300287 A300288 * A300290 A300291 A300292
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KEYWORD
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nonn,base
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AUTHOR
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Ivan N. Ianakiev, Mar 02 2018
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EXTENSIONS
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Escape clause added to definition by N. J. A. Sloane, Mar 03 2018
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STATUS
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approved
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