A362678 Contribution to the OEIS

 

A362678 Primes whose digits are prime and in nondecreasing order. 1

2, 3, 5, 7, 23, 37, 223, 227, 233, 257, 277, 337, 557, 577, 2237, 2333, 2357, 2377, 2557, 2777, 3557, 5557, 22277, 22777, 23333, 23357, 23557, 25577, 33377, 33577, 222337, 222557, 223337, 223577, 233357, 233557, 233777, 235577, 333337, 335557, 355777 (list; graph; refs; listen; history; edit; text; internal format)

OFFSET 1,1 COMMENTS Intersection of A009994 and A019546. The subsequence for primes whose digits are prime and in strictly increasing order has just eight terms: 2 3 5 7 23 37 257 2357 (see A177061). LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 MAPLE M:= 7: # for terms with <+ M digits R:= NULL: for d from 1 to M do S:= NULL: for x2 from 0 to d do for x3 from 0 to d-x2 do for x5 from 0 to d-x2-x3 do x7:= d-x2-x3-x5; x:= parse(cat(2$x2, 3$x3, 5$x5, 7$x7)); if isprime(x) then S:= S, x fi; od od od; R:= R, op(sort([S])); od: R; # Robert Israel, Jul 04 2023 MATHEMATICA Select[Prime[Range[31000]], AllTrue[d = IntegerDigits[#], PrimeQ] && LessEqual @@ d &] (* Amiram Eldar, Jul 07 2023 *) PROG (Python) from sympy import isprime from itertools import count, combinations_with_replacement as cwr, islice def agen(): yield from (filter(isprime, (int("".join(c)) for d in count(1) for c in cwr("2357", d)))) print(list(islice(agen(), 50))) # Michael S. Branicky, Jul 05 2023 (PARI) isok(p) = if (isprime(p), my(d=digits(p)); (d == vecsort(d)) && (#select(isprime, d) == #d)); \\ Michel Marcus, Jul 07 2023 CROSSREFS Cf. A009994, A019546, A177061. Sequence in context: A100552 A210566 A155873 * A106711 A235110 A048398 Adjacent sequences: A362675 A362676 A362677 * A362679 A362680 A362681 KEYWORD nonn,base AUTHOR James C. McMahon, Jul 03 2023 STATUS approved