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Number of ways to rearrange digits of prime(n)*prime(n+1) to form a prime.
2

%I #24 Aug 29 2024 18:46:24

%S 0,0,1,0,1,0,1,2,0,0,3,4,8,0,6,11,3,0,3,6,1,1,4,3,0,2,5,6,15,15,17,16,

%T 12,12,4,10,8,5,8,18,11,23,5,13,9,10,8,6,27,9,4,6,14,4,24,3,14,6,4,33,

%U 7,14,11,12,6,86,26,53,13,79,27,51,81,61,26,39,25,54,17,25

%N Number of ways to rearrange digits of prime(n)*prime(n+1) to form a prime.

%C Leading zeros are not allowed in the rearranged number.

%H Michael S. Branicky, <a href="/A053653/b053653.txt">Table of n, a(n) for n = 1..10000</a>

%e a(8) = 2 because 19*23 = 437 and 2 primes, 347 and 743, can be formed from the digits of 437.

%t nfp[n_]:=With[{id=IntegerDigits[n]},Length[Select[FromDigits/@Permutations[id],IntegerLength[ #] ==IntegerLength[n]&&PrimeQ[#]&]]]; nfp/@Times@@@Partition[Prime[Range[90]],2,1] (* _Harvey P. Dale_, Aug 29 2024 *)

%o (Python)

%o from sympy import isprime, prime

%o from sympy.utilities.iterables import multiset_permutations as mp

%o def c(s):

%o return sum(1 for t in mp(s) if t[0]!='0' and isprime(int("".join(t))))

%o def a(n): return c(str(prime(n)*prime(n+1)))

%o print([a(n) for n in range(1, 72)]) # _Michael S. Branicky_, Dec 22 2021

%Y Cf. A053652, A053736.

%K easy,nonn,look,base

%O 1,8

%A _Enoch Haga_, Feb 18 2000

%E Edited by _Jens Kruse Andersen_, Dec 01 2006