A217565 - OEIS

A217565

The smallest prime p that with its successor q gives prime counts of all ten base-10 digits for the expression (q^prime(n))*(p^prime(n+1)).

33581, 673, 571, 1987, 915199, 441799, 2115761, 961943, 15406687, 77123341, 4098427, 5526679, 54560189, 22291639, 371594479, 126499693, 229299227, 103196347, 37851677, 1198387109, 801422893, 966240103, 281430131, 926679973, 154019941, 196449137, 243985993

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OFFSET

1,1

COMMENTS

This reverses the idea for A217049, with the smaller of successive primes being raised to the larger prime power. See that sequence for motivation.

LINKS

Table of n, a(n) for n=1..27.

EXAMPLE

(677^3)*(673^5) is the value corresponding to a(2). What this means is that the decimal representation of this number has a prime number of copies of each digit and no pair of successive primes in the same order and smaller than {673,677} has the same characteristic.

MATHEMATICA

Table[p=2; While[!And@@PrimeQ[DigitCount[(p^Prime[n+1])*(NextPrime@p^Prime[n])]], p=NextPrime@p]; p, {n, 6}] (* Giorgos Kalogeropoulos, Aug 18 2021 *)

PROG

(Python)

from sympy import isprime, nextprime, prime

from sympy.ntheory import count_digits

def a(n):

pn = prime(n); qn = nextprime(pn)

p, q = 2, 3; c = count_digits((q**pn)*(p**qn))

while not all(isprime(c[i]) for i in range(10)):

p, q = q, nextprime(q); c = count_digits((q**pn)*(p**qn))

return p

print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Aug 21 2021

CROSSREFS