A307714 Product of digits is noncomposite.

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

Author

M. F. Hasler, Apr 23 2019

Keywords

• nonn
• base

Comments

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.

Crossrefs

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

Programs

PARI

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))