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A307714
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Product of digits is noncomposite.
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0
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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PROG
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(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)))}
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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