A260716 - OEIS

%I #10 Aug 06 2015 07:42:21

%S 6,4,55,141,2,2,4,5,3,4,3,14,2,1,4,3,1,18,6,3,17,36,1,10,13,1,10,2,2,

%T 86,27,7,4,50,1,4,6,4,3,13,7,3,1,207,2,7,10,10,128,7,2,4,2,9,20,2,15,

%U 24,3,10,64,7,4,4,1,4,15,8,4,1,45,3,2,1,1,2,6,28,1,2,11,1,3,14,13,3,11,12,4,28,3,7,55,40,9,4,51,5,2,6,1,2,1,15,1

%N a(n) = number of iterations of A234742 needed when starting from A091209(n) before a fixed point is reached.

%C It is not known whether the sequence is well-defined for all values. For example, does a(144) have a finite value? Cf. the sequence A260441, starting iteration from 1361 = A091209(144).

%H Antti Karttunen, <a href="/A260716/b260716.txt">Table of n, a(n) for n = 1..143</a>

%F a(n) = A260712(A091209(n)).

%o (PARI)

%o allocatemem((2^29));

%o v091209 = [5, 17, 23, 29, 43, 53, 71, 79, 83, 89, 101, 107, 113, 127, 139, 149, 151, 163, 173, 179, 181, 197, 199, 223, 227, 233, 251, 257, 263, 269, 271, 277, 281, 293, 307, 311, 317, 331, 337, 347, 349, 353, 359, 367, 373, 383, 389, 401, 409, 421, 431, 439, 443, 449, 457, 461, 467, 479, 491, 503, 509, 521, 523, 541, 547, 569, 571, 577, 593, 599, 619, 641, 643, 653, 659, 673, 683, 691, 709, 727, 733, 739, 743, 751, 773, 797, 809, 811, 821, 823, 829, 839, 853, 857, 863, 881, 887, 907, 919, 937, 941, 947, 977, 983, 991, 997, 1009, 1013, 1021, 1031, 1049, 1061, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1129, 1151, 1171, 1181, 1187, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1283, 1289, 1297, 1301, 1303, 1307, 1319, 1321, 1327];

%o A091209(n) = v091209[n];

%o A234742(n) = factorback(subst(lift(factor(Mod(1, 2)*Pol(binary(n)))), x, 2)); \\ After _M. F. Hasler_'s Feb 18 2014 code.

%o A260712(n) = {my(prev=-1,i=-1); until((n==prev), prev = n; n = A234742(n); i++); return(i); }

%o A260716(n) = A260712(A091209(n));

%o for(n=1, 143, write("b260716.txt", n, " ", A260716(n)));

%o (Scheme) (define (A260716 n) (A260712 (A091209 n)))

%Y Cf. A091209, A234742, A260712, A260713, A260441.

%K nonn

%O 1,1

%A _Antti Karttunen_, Aug 04 2015