A053652 -id:A053652 - cp's OEIS frontend

A053653 Number of ways to rearrange digits of prime(n)*prime(n+1) to form a prime.

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

Offset: 1

Enoch Haga, Feb 18 2000

Leading zeros are not allowed in the rearranged number.

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

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A053652, A053736.

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 *)

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)))
print([a(n) for n in range(1, 72)]) # Michael S. Branicky, Dec 22 2021

Edited by Jens Kruse Andersen, Dec 01 2006

A053736 Run through primes p; if the digits of p*q (where q is the prime following p) can be rearranged to form one or more primes r, append these primes r to the sequence.

Original entry on oeis.org

53, 431, 233, 347, 743, 1471, 1741, 7411, 1571, 5171, 5711, 7151, 1367, 1637, 3167, 3617, 3671, 3761, 6173, 6317, 1249, 1429, 4129, 4219, 9241, 9421, 1237, 1327, 1723, 2137, 2371, 2713, 2731, 3217, 3271, 7213, 7321, 5399, 5939, 9539

Offset: 1

Enoch Haga, Feb 13 2000

Leading zeros are not allowed in the rearranged number.

			7*11=77, but no prime rearrangements are possible; 11*13 is 143, whose digits can be rearranged to 431, a prime.

C. A. Pickover, "Vampire numbers," chapter 30 of Keys to Infinity. NY: Wiley, 1995. Pages 227-231

A053652 gives the entries sorted and with duplicates removed. Cf. A014575, A053652.

Corrected and extended by Jens Kruse Andersen, Dec 01 2006

cp's OEIS Frontend

A053653 Number of ways to rearrange digits of prime(n)*prime(n+1) to form a prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

Extensions