|
|
A053653
|
|
Number of ways to rearrange digits of prime(n)*prime(n+1) to form a prime.
|
|
2
|
|
|
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, 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, 7, 14, 11, 12, 6, 86, 26, 53, 13, 79, 27, 51, 81, 61, 26, 39, 25, 54, 17, 25
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,8
|
|
COMMENTS
|
Leading zeros are not allowed in the rearranged number.
|
|
LINKS
|
|
|
EXAMPLE
|
a(8) = 2 because 19*23 = 437 and 2 primes, 347 and 743, can be formed from the digits of 437.
|
|
MATHEMATICA
|
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 *)
|
|
PROG
|
(Python)
from sympy import isprime, prime
from sympy.utilities.iterables import multiset_permutations as mp
def c(s):
return sum(1 for t in mp(s) if t[0]!='0' and isprime(int("".join(t))))
def a(n): return c(str(prime(n)*prime(n+1)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,look,base,changed
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|