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A117835 Prime numbers for which the product of the digits is a noncomposite number. 3


%S 2,3,5,7,11,13,17,31,71,113,131,151,211,311,1117,1151,1171,1511,2111,

%T 11113,11117,11131,11171,11311,111121,111211,112111,113111,131111,

%U 311111,511111,1111151,1111211,1111711,1117111,1171111,11111117,11111131,11111171,11111311,11113111,11131111

%N Prime numbers for which the product of the digits is a noncomposite number.

%C 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.

%C 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

%C Contains primes in A028842 as a subset. - _M. F. Hasler_, Apr 23 2019

%F A117835 = { n in A008578 | A007954(n) is again in A008578 }. - _M. F. Hasler_, Apr 23 2019

%o (PARI) From _M. F. Hasler_, Apr 23 2019: (Start)

%o select( is_A117835(n)=isprime(n)&&(isprime(n=vecprod(digits(n)))||n==1), [0..999]) \\ In older PARI versions, vecprod=factorback.

%o 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}

%o A117835_vec(N=99)=vector(N,i,t=next_A117835(if(i>1,t))) \\ (End)

%Y Cf. A046703 ("prime" variant), A007954 (product of digits), A008578 (noncomposite numbers), A028842 (product of digits is prime).

%K base,nonn

%O 1,1

%A Luc Stevens (lms022(AT)yahoo.com), Apr 30 2006

%E Name changed, following a remark from _Zak Seidov_, and edited by _M. F. Hasler_, Apr 22 2019

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Last modified September 30 23:44 EDT 2020. Contains 337440 sequences. (Running on oeis4.)