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

1,3

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

R:= 0:
for d from 1 to 6 do
  t:= (10^d-1)/9;
  R:= R, t, seq(seq(t + a*10^i, a=[1, 2, 4, 6]), i=0..d-1);
od:
R; # Robert Israel, Mar 05 2026

Prog

(PARI) select( is(n)={isprime(n=vecprod(digits(n)))||n==1}, [0..1999]) \\ In older PARI versions, vecprod=factorback.
(PARI) 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))

Crossrefs

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

Sequence in context: A384735 A230918 A001742 * A369254 A073085 A340657

Adjacent sequences: A307711 A307712 A307713 * A307715 A307716 A307717

Keyword

nonn,base

Author

M. F. Hasler, Apr 23 2019

Status

approved