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A117835
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Prime numbers for which the product of the digits is a noncomposite number.
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3
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2, 3, 5, 7, 11, 13, 17, 31, 71, 113, 131, 151, 211, 311, 1117, 1151, 1171, 1511, 2111, 11113, 11117, 11131, 11171, 11311, 111121, 111211, 112111, 113111, 131111, 311111, 511111, 1111151, 1111211, 1111711, 1117111, 1171111, 11111117, 11111131, 11111171, 11111311, 11113111, 11131111
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OFFSET
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1,1
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COMMENTS
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None of the numbers in the sequence can have a digit 0, 4, 6, 8 or 9. The digits are all 1's, or there is one digit 2, 3, 5 or 7 and all the others are 1's.
A variant of A046703 where the "all '1's" (repunit primes R(k) with k in A004023: R(2) = 11, R(19), ...) are excluded. - M. F. Hasler, Apr 22 2019
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LINKS
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FORMULA
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PROG
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select( is_A117835(n)=isprime(n)&&(isprime(n=vecprod(digits(n)))||n==1), [0..999]) \\ In older PARI versions, vecprod=factorback.
next_A117835(n)={until( isprime(n), my(d=digits(n)); n=if(n<3||Set(d)==[1], n+1, fromdigits(apply(t->if(t<2, 1, t<7, nextprime(t+1), 11), d)))); n}
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), Apr 30 2006
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EXTENSIONS
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STATUS
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approved
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