prog.sf

#!/usr/bin/ruby

# a(1)=1; a(n+1) = the smallest prime divisor of A138793(n+1).
# https://oeis.org/A138962

# First several terms of the sequence:
#   1, 3, 3, 29, 3, 3, 19, 3, 3, 457, 3, 3, 16087, 3, 3, 35963, 3, 3, 167, 3, 3, 7, 3, 3, 13, 3, 3, 953, 3, 3, 7, 3, 3, 548636579, 3, 3, 19, 3, 3, 71, 3, 3, 13, 3, 3, 89, 3, 3, 114689, 3, 3, 17, 3, 3, 12037, 3, 3, 7, 3, 3

# a(n) = A020639(A138793(n)). - ~~~~

include("../../../factordb/auto.sf")

func a(n) {
    1..n -> join.flip.to_i
}

var bfile = File("bfile.txt").open_w.autoflush(true)

for n in (1..10000) {
    #next if (n < 325)
    var k = a(n)
    if (n == 310) {
        k = 4931885197913
    }
    if (n == 331) {
        k = 244191703201
    }
    #~ if (n == 334) {   # conjecture
        #~ k = 153309577604336551
    #~ }
    var row = "#{n} #{lpf(k)||1}"
    say row
    bfile.say(row)
}

__END__


# PARI/GP program:

f(n) = my(D = Vec(concat(apply(s->Str(s), [1..n])))); eval(concat(vector(#D, k, D[#D-k+1]))); \\ A138793
a(n) = my(k=f(n)); forprime(p=2, 10^6, if(k%p == 0, return(p))); if(n == 1, 1, vecmin(factor(k)[,1])); \\ ~~~~