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A120716 a(1)=1, a(p)=p if p is a prime. Otherwise, start with n and iterate the map (k -> concatenation of nontrivial divisors of k) until we reach a prime q; then a(n) = q. If we never reach a prime, a(n) = -1.

%I A120716 #22 Mar 14 2023 03:35:15
%S A120716 1,2,3,2,5,23,7
%N A120716 a(1)=1, a(p)=p if p is a prime. Otherwise, start with n and iterate the map (k -> concatenation of nontrivial divisors of k) until we reach a prime q; then a(n) = q. If we never reach a prime, a(n) = -1.
%C A120716 a(8) is currently unknown.
%C A120716 The sequence continues from a(8)-a(100): >10^50, 3, 5, 11, >10^50, 13, 313, 1129, >10^50, 17, >10^50, 19, >10^50, 37, 211, 23, >10^50, 5, 3251, 313, >10^50, 29, >10^50, 31, >10^50, 311, >10^50, 1129, >10^50, 37, 373, 313, >10^50, 41, >10^50, 43, >10^50, >10^50, 223, 47, >10^50, 7, >10^50, 317, >10^50, 53, 23691827, 773, >10^50, 1129, 229, 59, >10^50, 61, >10^50, 378593, >10^50, >10^5", >10^50, 67, >10^50, 39191573, >10^50, 71, >10^50, 73, 379, >10^50, >10^50, 3979237, 236132639, 79, >10^50, >10^50, 241, 83, >10^50, 3137, >10^50, 3983249, >10^50, 89, >10^50, >10^50, >10^50, 331, 1319, 36389, >10^50, 97, >10^50, 391133, >10^50. - _Robert Price_, Mar 27 2019
%H A120716 N. J. A. Sloane et al., <a href="/A120716/a120716.txt">Notes on the attempt to find a(8)</a>
%e A120716 4 -> 2, prime, so a(4) = 2.
%e A120716 6 -> 2,3 -> 23, prime, so a(6) = 23.
%e A120716 8 -> 2,4 -> 24 -> 2,3,4,6,8,12 -> 2346812 -> 2,4,13,26,52,45131,90262,180524,586703,1173406 -> 2413265245131902621805245867031173406 -> ? (see link for the continuation)
%e A120716 9 -> 3, prime, so a(9) = 3.
%e A120716 21 -> 3,7 -> 37, prime, so a(21) = 37.
%t A120716 A120716[n_] := Module[{x},
%t A120716    If[n == 1, Return[1]];
%t A120716    If[PrimeQ[n], Return[n]];
%t A120716    x = FromDigits[Flatten[IntegerDigits[Rest[Most[Divisors[n]]]]]];
%t A120716    If[x > 10^50, Return[">10^50"], A120716[x]]];
%t A120716 Table[A120716[n], {n, 1, 100}] (* _Robert Price_, Mar 27 2019 *)
%Y A120716 Cf. A120712, A120713, A037274, A037279, A130139 (a bisection), A130140, A130141, A130142.
%K A120716 nonn,base,more,hard
%O A120716 1,2
%A A120716 _N. J. A. Sloane_, Jul 19 2007
%E A120716 Edited by _Michel Marcus_, Mar 09 2023