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A117835 Prime numbers for which the product of the digits is a noncomposite number. 3
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 (list; graph; refs; listen; history; text; internal format)
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

PROG

(PARI) From  M. F. Hasler, Apr 23 2019: (Start)

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}

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

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

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Last modified August 14 04:13 EDT 2020. Contains 336477 sequences. (Running on oeis4.)