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A130139 Let f denote the map that replaces k with the concatenation of its nontrivial divisors, written in increasing order, each divisor being written in base 10 in the normal way. Then a(n) = prime reached when starting at 2n+1 and iterating f.

%I A130139 #24 Mar 09 2023 08:40:45
%S A130139 1,3,5,7,3,11,13,1129,17,19,37,23,5,313,29,31,311,1129,37,313,41,43
%N A130139 Let f denote the map that replaces k with the concatenation of its nontrivial divisors, written in increasing order, each divisor being written in base 10 in the normal way. Then a(n) = prime reached when starting at 2n+1 and iterating f.
%C A130139 If 2n+1 is 1 or a prime, set a(n) = 2n+1. If no prime is ever reached, set a(n) = -1.
%e A130139 n = 7: 2n+1 = 15 = 3*5 -> 35 = 5*7 -> 57 = 3*19 -> 319 = 11*29 -> 1129, prime, so a(7) = 1129.
%o A130139 (Python)
%o A130139 from sympy import divisors, isprime
%o A130139 def f(n): return int("".join(str(d) for d in divisors(n)[1:-1]))
%o A130139 def a(n):
%o A130139     if n == 0: return 1
%o A130139     fn, c = 2*n + 1, 0
%o A130139     while not isprime(fn):
%o A130139         fn, c = f(fn), c+1
%o A130139     return fn
%o A130139 print([a(n) for n in range(22)]) # _Michael S. Branicky_, Jul 11 2022
%Y A130139 Cf. A037279, A130140, A130141, A130142. A bisection of A120716.
%K A130139 nonn,base,more
%O A130139 0,2
%A A130139 _N. J. A. Sloane_, Jul 30 2007
%E A130139 Name edited by _Michel Marcus_, Mar 09 2023