A068831 Primes with all odd digits such that the next three primes also contain all odd digits.

3, 5, 7, 11, 191, 311, 313, 9133, 9371, 11113, 11171, 15731, 15937, 15959, 17939, 17957, 19319, 19553, 19739, 19973, 19979, 31151, 31333, 31511, 33353, 35573, 35753, 39113, 39119, 39937, 51131, 51133, 51971, 53717, 53719, 53731, 55313, 55331

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2554

Example

313 belongs to this sequence as the next three primes 317, 331 and 337 contain only odd digits.

Mathematica

odQ[n_] := And @@ OddQ[Flatten[IntegerDigits[Join[{n}, Table[NextPrime[n, k], {k, 3}]]]]]; Select[Prime[Range[5700]], odQ] (* Jayanta Basu, Aug 07 2013 *)
Prime[#]&/@SequencePosition[Table[If[AllTrue[IntegerDigits[p], OddQ], 1, 0], {p, Prime[Range[ 6000]]}], {1, 1, 1, 1}][[;; , 1]] (* Harvey P. Dale, Apr 02 2023 *)

Prog

(Magma) [NthPrime(n): n in [1..10^4] | forall{NthPrime(n+i): i in [0..3] | Intseq(NthPrime(n+i)) subset [1..9 by 2]}]; // Bruno Berselli, Aug 08 2013
(Python)
from itertools import product
from sympy import isprime, nextprime
A068831_list = [p for p in (int(''.join(d)) for l in range(1, 9) for d in product('13579', repeat=l)) if isprime(p) and set(str(nextprime(p, 1))) <= {'1', '3', '5', '7', '9'} and set(str(nextprime(p, 2))) <= {'1', '3', '5', '7', '9'} and set(str(nextprime(p, 3))) <= {'1', '3', '5', '7', '9'} ] # Chai Wah Wu, Aug 13 2015

Crossrefs

Cf. A068830, A068832.

Sequence in context: A088051 A159471 A068113 * A109862 A069804 A245722

Adjacent sequences: A068828 A068829 A068830 * A068832 A068833 A068834

Keyword

nonn,base

Author

Amarnath Murthy, Mar 09 2002

Extensions

Missing term a(19)=19739 supplied by Jayanta Basu, Aug 07 2013

Status

approved