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A217049
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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Motivation for this sequence stems from the coincidence that (2^41)*(3^43) and (3^43)*(5^47) give prime counts for their digits.
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LINKS
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EXAMPLE
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(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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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