A071712 The 23-step cycle reached for any initial value k less than 100000, after iterations of sopf(8x+1), where sopf(n) denote the sum of the prime factors of n (sopf(12) = 2+2+3 = 7).

66, 46, 47, 42, 337, 63, 106, 286, 119, 953, 76, 39, 313, 175, 470, 3761, 30089, 367, 103, 24, 193, 111, 134

Offset

1,1

Comments

If x>100000 is there another cycle?

No other cycle found below 10^8. - Michel Marcus, Nov 27 2013

Links

Table of n, a(n) for n=1..23.

K. S. Brown, Linear Sum of Prime Factors

Prog

(PARI) iscycle(v, nextn) = {for (i=1, #v, if (v[i] == nextn, return (1); ); ); return (0); }
fcycle(n, known) = {v = vector(1); v[1] = n; first = n; while((nextn = soph(n)) <= first, if (vecsearch(known, nextn), return([])); if (iscycle(v, nextn), return (v)); v = concat(v, nextn); n = nextn; ); return ([]); }
fcycles(na, nb) = {known = [30089]; known = []; for(n = na, nb, v = fcycle(n, known); if (#v, print(v, ", "); return(); ); ); } \\ Displays sequence terms or search for higher cycle, depending on the order of the 2 "known=" lines. - Michel Marcus, Nov 29 2013

Crossrefs

Cf. A001414.

Sequence in context: A138843 A033386 A008896 * A080592 A059175 A031960

Adjacent sequences: A071709 A071710 A071711 * A071713 A071714 A071715

Keyword

nonn,fini,full

Author

Benoit Cloitre, Jun 03 2002

Status

approved