A053736 -id:A053736 - cp's OEIS frontend

A053652 Primes for which some rearrangement of the digits (leading zeros not allowed) is the product of two consecutive primes.

53, 233, 347, 431, 743, 1237, 1249, 1327, 1367, 1429, 1471, 1571, 1583, 1637, 1723, 1741, 2137, 2371, 2713, 2731, 3167, 3217, 3271, 3581, 3617, 3671, 3761, 3851, 3863, 3877, 4129, 4219, 5171, 5381, 5399, 5477, 5657, 5711, 5813, 5939

Offset: 1

Enoch Haga, Feb 18 2000

Primes from A053736 sorted in numerical order.

			a(3)=347, a(5)=743. These terms are derived from 19*23=437. By arranging digits of 437, two primes are formed: 347 and 743.

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

Cf. A053736, A053653, A014575.

Edited by Jens Kruse Andersen, Dec 01 2006

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

Original entry on oeis.org

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

cp's OEIS Frontend

A053652 Primes for which some rearrangement of the digits (leading zeros not allowed) is the product of two consecutive primes.

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

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