cp's OEIS Frontend

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

%I A117835 #26 Sep 27 2024 11:20:28
%S A117835 2,3,5,7,11,13,17,31,71,113,131,151,211,311,1117,1151,1171,1511,2111,
%T A117835 11113,11117,11131,11171,11311,111121,111211,112111,113111,131111,
%U A117835 311111,511111,1111151,1111211,1111711,1117111,1171111,11111117,11111131,11111171,11111311,11113111,11131111
%N A117835 Prime numbers for which the product of the digits is a noncomposite number.
%C A117835 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 A117835 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 A117835 Contains primes in A028842 as a subset. - _M. F. Hasler_, Apr 23 2019
%F A117835 A117835 = { n in A008578 | A007954(n) is again in A008578 }. - _M. F. Hasler_, Apr 23 2019
%t A117835 Select[Prime[Range[10^6]],PrimeQ[Times@@IntegerDigits[#]]||Times@@IntegerDigits[#]==1&] (* _James C. McMahon_, Sep 24 2024 *)
%o A117835 (PARI)
%o A117835 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
%o A117835 (PARI)
%o A117835 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 A117835_vec(N=99)=vector(N,i,t=next_A117835(if(i>1,t))) \\ _M. F. Hasler_, Apr 23 2019
%Y A117835 Cf. A046703 ("prime" variant), A007954 (product of digits), A008578 (noncomposite numbers), A028842 (product of digits is prime).
%K A117835 base,nonn
%O A117835 1,1
%A A117835 Luc Stevens (lms022(AT)yahoo.com), Apr 30 2006
%E A117835 Name changed, following a remark from _Zak Seidov_, and edited by _M. F. Hasler_, Apr 22 2019