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A217049 Least prime p such that all ten base-10 digits have prime counts in (p^prime(n))*(q^prime(n+1)), where q is the next prime after p. 1
18329, 1913, 1063, 109, 932839, 85061, 29729989, 5653759, 1958731, 20891539, 35008723, 28265837, 2, 3, 6238777, 276624683, 92343187, 24205651, 49598321, 17722981, 46741657, 219329923, 297614029, 106791577, 621528749, 217893821, 113824657, 122670287, 81263857 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Motivation for this sequence stems from the coincidence that (2^41)*(3^43) and (3^43)*(5^47) give prime counts for their digits.
LINKS
EXAMPLE
(18329^2)*(18341^3) = 2072748335390985614861 has digit counts [2,2,2,3,2,2,2,2,3,2], all primes, and replacing the pair (18329,18341) with a smaller pair fails this criterion. In particular, (3733^2)*(3739^3) = 728420861672094091 has digit counts [3,2,3,0,2,0,2,2,2,2], not all prime.
MATHEMATICA
Table[p=2; While[!And@@PrimeQ[DigitCount[(p^Prime@n)*(NextPrime@p^Prime[n+1])]], 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(p**pn*q**qn)
while not all(isprime(c[i]) for i in range(10)):
p, q = q, nextprime(q); c = count_digits(p**pn*q**qn)
return p
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Aug 20 2021
CROSSREFS
Cf. A216854.
Sequence in context: A237737 A145822 A286035 * A251025 A203783 A071368
KEYWORD
nonn,base
AUTHOR
James G. Merickel, Sep 25 2012
EXTENSIONS
Name clarified by Tanya Khovanova, Aug 17 2021
a(23)-a(29) from Michael S. Branicky, Aug 25 2021
Name edited by Michel Marcus and Michael S. Branicky, Aug 25 2021
STATUS
approved

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Last modified June 25 04:03 EDT 2024. Contains 373697 sequences. (Running on oeis4.)