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A307714
Product of digits is noncomposite.
0
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.
PROG
(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))
CROSSREFS
Cf. A008578 (noncomposite numbers), A002275 (repunits), A117835 (primes in this sequence).
Sequence in context: A131930 A230918 A001742 * A369254 A073085 A340657
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Apr 23 2019
STATUS
approved