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

1,1

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

Links

Table of n, a(n) for n=1..42.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A186307 A321420 A118725 * A120639 A141263 A016114

Adjacent sequences: A117832 A117833 A117834 * A117836 A117837 A117838

Keyword

base,nonn

Author

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

Extensions

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

Status

approved