prog.sf

#!/usr/bin/ruby

# Smallest palindrome in base 10 whose factorization contains n distinct base 10 palindromic prime factors.
# https://oeis.org/A335934

# Known terms:
#   1, 2, 6, 66, 2772, 279972, 67566576, 5159488849515, 83797355379738

# Palindromes with exactly n distinct palindromic prime factors:
#   f(8) = 2459090770909542

# See also:
#   http://www.worldofnumbers.com/assign3.htm


#`( PARI/GP program:

omega_palindromes(A, B, n) = A=max(A, vecprod(primes(n))); (f(m, p, j) = my(list=List()); forprime(q=p, sqrtnint(B\m, j), if(q == 5 && m%2 == 0, next); if(fromdigits(Vecrev(digits(q))) != q, next); my(v=m*q); while(v <= B, if(j==1, if(v>=A && fromdigits(Vecrev(digits(v))) == v, 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) = if(n==0, return(1)); my(x=vecprod(primes(n)), y=2*x); while(1, my(v=omega_palindromes(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ ~~~~

)