A177061 - OEIS

%I #22 Sep 09 2023 21:59:36

%S 2,3,5,7,23,37,53,73,257,523,2357,2753,3257,3527,5237,5273,7253,7523

%N Primes p formed from single-digit primes only, each used at most once.

%C 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).

%C 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

%C 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

%D E. I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig/Jena/Berlin 1982

%e 3//7 = 37 = prime(12) is the 6th term.

%e 2//3//5//7 = 2357 = prime(350) is the 11th term

%e p = 7//5//2//3 = 7523 = prime(953) = A033548(59) is the last term.

%t Select[FromDigits/@Flatten[Permutations/@Subsets[{2,3,5,7}],1],PrimeQ]// Union (* _Harvey P. Dale_, Sep 08 2021 *)

%o (PARI) isok(p) = {my(d = digits(p)); if (#d == #Set(d) && vecmin(apply(isprime, d)) == 1, return (1)); return(0);}

%o lista() = {forprime(p=1, 100000, if (isok(p), print1(p, ", ")););} \\ _Michel Marcus_, Aug 07 2020

%Y Cf. A000040, A168349, A168385, A347612

%K easy,base,fini,full,nonn

%O 1,1

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 02 2010

%E Edited by Assoc. Eds. OEIS, May 09 2010

%E Missing term 5273 added by _Eren Donmez_, Aug 07 2020

%E Cross reference added by _Harvey P. Dale_, Sep 09 2021