A117835 -id:A117835 - cp's OEIS frontend

A046703 Multiplicative primes: product of digits is a prime.

2, 3, 5, 7, 13, 17, 31, 71, 113, 131, 151, 211, 311, 1117, 1151, 1171, 1511, 2111, 11113, 11117, 11131, 11171, 11311, 111121, 111211, 112111, 113111, 131111, 311111, 511111, 1111151, 1111211, 1111711, 1117111, 1171111, 11111117, 11111131, 11111171, 11111311, 11113111, 11131111

Offset: 1

Felice Russo

Primes with one prime digit and all other digits are 1. The linked table includes probable primes. - Jens Kruse Andersen, Jul 21 2014

Jens Kruse Andersen, Table of n, a(n) for n = 1..1000

Cf. A117835 ("noncomposite" variant), A007954 (product of digits), A028842 (product of digits is prime).

Select[Prime[Range[740000]],PrimeQ[Times@@IntegerDigits[#]]&] (* Harvey P. Dale, Oct 02 2011 *)
Select[FromDigits/@Flatten[Table[Permutations[PadRight[{p},n,1]],{n,8},{p,{2,3,5,7}}],2],PrimeQ]//Union (* Harvey P. Dale, Nov 21 2019 *)

f(n,b,d) = if(d, f(10*n+1, b, d-1); if(!b, forprime(q=2, 9, f(10*n+q, 1, d-1))), if(b && isprime(n), print1(n", ")))
for(d=1, 8, f(0,0,d)) \\ f(0,0,d) prints d-digit terms. Jens Kruse Andersen, Jul 21 2014

\\ From M. F. Hasler, Apr 23 2019: (Start)
select( is_A046703(n)=isprime(vecprod(digits(n)))&&ispseudoprime(n), [0..9999]) \\ This defines is_A046703(). In older PARI versions, vecprod=factorback.
next_A046703(n)={if( n>1, until( ispseudoprime(n), my(d=digits(n)); n=fromdigits( apply( t->if(t>1, nextprime(t+1), 1), d))+(d[1]>5)); n, 2)}
A046703_vec(N=99)=vector(N, i, t=next_A046703(if(i>1, t))) \\ (End)

Corrected by Harvey P. Dale, Oct 02 2011

A307714 Product of digits is noncomposite.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 11, 12, 13, 15, 17, 21, 31, 51, 71, 111, 112, 113, 115, 117, 121, 131, 151, 171, 211, 311, 511, 711, 1111, 1112, 1113, 1115, 1117, 1121, 1131, 1151, 1171, 1211, 1311, 1511, 1711, 2111, 3111, 5111, 7111, 11111, 11112, 11113, 11115, 11117, 11121, 11131, 11151, 11171, 11211

Offset: 1

M. F. Hasler, Apr 23 2019

Either all digits are '1', or one of the digits can be a prime (2, 3, 5, 7).
The initial 0 is included by convention. (Some authors consider that the decimal expansion of 0 is the empty sum (0 has no digits) whence the product of digits is 1.)
This is the union of repunits A002275 and numbers whose product of digit is prime, A028842.

Cf. A008578 (noncomposite numbers), A002275 (repunits), A117835 (primes in this sequence).

select( is(n)={isprime(n=vecprod(digits(n)))||n==1}, [0..1999]) \\ In older PARI versions, vecprod=factorback.
next_A307714(n,d)={if(n<3||Set(d=digits(n))==[1], n+1, fromdigits(apply(t->if(t<2, 1, t<7, nextprime(t+1),11), d)))}
A307714_vec(N=99)=vector(N,i,t=if(i>1,next_A307714(t),0))

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A046703 Multiplicative primes: product of digits is a prime.

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A307714 Product of digits is noncomposite.

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