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%I #10 Dec 08 2019 02:10:22
%S 0,1,2,3,5,7,11,12,13,15,17,21,31,51,71,111,112,113,115,117,121,131,
%T 151,171,211,311,511,711,1111,1112,1113,1115,1117,1121,1131,1151,1171,
%U 1211,1311,1511,1711,2111,3111,5111,7111,11111,11112,11113,11115,11117,11121,11131,11151,11171,11211
%N Product of digits is noncomposite.
%C Either all digits are '1', or one of the digits can be a prime (2, 3, 5, 7).
%C 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.)
%C This is the union of repunits A002275 and numbers whose product of digit is prime, A028842.
%o (PARI) select( is(n)={isprime(n=vecprod(digits(n)))||n==1}, [0..1999]) \\ In older PARI versions, vecprod=factorback.
%o 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)))}
%o A307714_vec(N=99)=vector(N,i,t=if(i>1,next_A307714(t),0))
%Y Cf. A008578 (noncomposite numbers), A002275 (repunits), A117835 (primes in this sequence).
%K nonn,base
%O 1,3
%A _M. F. Hasler_, Apr 23 2019
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