OFFSET
1,1
COMMENTS
List of (p,i): (2,1), (3,2), (5,3), (7,4), (23,9), (37,12), (53,16), (73,21), (257,55), (523,99), (2357,350), (2753,402), (3257,460), (3527,492), (5237,697), (5273, 699), (7253,928), (7523,953).
There are exactly eight primes whose digits are primes in strictly increasing order: 2, 3, 5, 7, 23, 37, 257, 2357. - James C. McMahon, Jul 04 2023
There are exactly six primes whose digits are primes in strictly decreasing order: 2, 3, 5, 7, 53, 73. - James C. McMahon, Aug 09 2023
REFERENCES
E. I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig/Jena/Berlin 1982
EXAMPLE
3//7 = 37 = prime(12) is the 6th term.
2//3//5//7 = 2357 = prime(350) is the 11th term
p = 7//5//2//3 = 7523 = prime(953) = A033548(59) is the last term.
MATHEMATICA
Select[FromDigits/@Flatten[Permutations/@Subsets[{2, 3, 5, 7}], 1], PrimeQ]// Union (* Harvey P. Dale, Sep 08 2021 *)
PROG
(PARI) isok(p) = {my(d = digits(p)); if (#d == #Set(d) && vecmin(apply(isprime, d)) == 1, return (1)); return(0); }
lista() = {forprime(p=1, 100000, if (isok(p), print1(p, ", ")); ); } \\ Michel Marcus, Aug 07 2020
CROSSREFS
KEYWORD
easy,base,fini,full,nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 02 2010
EXTENSIONS
Edited by Assoc. Eds. OEIS, May 09 2010
Missing term 5273 added by Eren Donmez, Aug 07 2020
Cross reference added by Harvey P. Dale, Sep 09 2021
STATUS
approved