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A239696
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Smallest number m such that m and reverse(m) each have exactly n distinct prime factors.
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2
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2, 6, 66, 858, 6006, 204204, 10444434, 208888680, 6172882716, 231645546132, 49795711759794, 2400532020354468, 477566276048801940, 24333607174192936620
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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The first nontrivial example is a(6) = 204204. 204204 = 2^2*3*7*11*13*17 (6 distinct prime factors). 402402 = 2*3*7*11*13*67 (6 distinct prime factors). Since 204204 is the smallest number with this property, a(6) = 204204.
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PROG
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(Python)
import sympy
from sympy import factorint
def Rev(x):
..rev = ''
..for i in str(x):
....rev = i + rev
..return int(rev)
def RevFact(x):
..n = 2
..while n < 10**8:
....if len(list(factorint(n).values())) == x:
......if len(list(factorint(Rev(n)).values())) == x:
........return n
......else:
........n += 1
....else:
......n += 1
x = 1
while x < 50:
..print(RevFact(x))
..x += 1
(PARI)
generate(A, B, n) = A=max(A, vecprod(primes(n))); (f(m, p, j) = my(list=List()); forprime(q=p, sqrtnint(B\m, j), my(v=m*q); while(v <= B, if(j==1, if(v>=A && omega(fromdigits(Vecrev(digits(v)))) == n, listput(list, v)), if(v*(q+1) <= B, list=concat(list, f(v, q+1, j-1)))); v *= q)); list); vecsort(Vec(f(1, 2, n)));
a(n) = my(x=vecprod(primes(n)), y=2*x); while(1, my(v=generate(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Feb 07 2023
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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