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

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

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

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

Contains primes in A028842 as a subset. - M. F. Hasler, Apr 23 2019

Crossrefs

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

Programs

Mathematica

Select[Prime[Range[10^6]],PrimeQ[Times@@IntegerDigits[#]]||Times@@IntegerDigits[#]==1&] (* James C. McMahon, Sep 24 2024 *)

PARI

select( is_A117835(n)=isprime(n)&&(isprime(n=vecprod(digits(n)))||n==1), [0..999]) \\ In older PARI versions, vecprod=factorback. \\ M. F. Hasler, Apr 23 2019

PARI

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}
A117835_vec(N=99)=vector(N,i,t=next_A117835(if(i>1,t))) \\ M. F. Hasler, Apr 23 2019

Formula

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

Extensions

Name changed, following a remark from Zak Seidov, and edited by M. F. Hasler, Apr 22 2019