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 A193230 Start with 1; if even, divide by 2; if odd, add the next three primes. 6
 1, 11, 60, 30, 15, 74, 37, 168, 84, 42, 21, 104, 52, 26, 13, 72, 36, 18, 9, 50, 25, 122, 61, 272, 136, 68, 34, 17, 88, 44, 22, 11, 60, 30, 15, 74, 37, 168, 84, 42, 21, 104, 52, 26, 13, 72, 36, 18, 9, 50, 25, 122, 61, 272, 136, 68, 34, 17, 88, 44, 22, 11, 60, 30, 15, 74, 37, 168, 84, 42, 21, 104, 52, 26, 13, 72, 36, 18, 9, 50, 25, 122, 61, 272, 136, 68, 34, 17, 88, 44, 22, 11, 60, 30, 15, 74, 37, 168, 84, 42, 21, 104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Trajectory of 1 under the map x -> A174221(x). Periodic with period of length 30, starting at a(2) = 11. Angelini conjectures that the orbit under A174221 becomes periodic for any initial value. He calls this the PrimeLatz conjecture, as tribute to L. Collatz, known for the 3n+1 conjecture. It has been checked that the loop (11, ..., 22) (or (9, ..., 18), to start with the smallest element) is the only loop (except for the fixed point 0) at least up to values not exceeding 10^8, and the orbit of every positive integer <= 10^4 does end in this loop. - M. F. Hasler, Oct 25 2017 It might have been more natural to start this sequence with offset 0. Since a(n) = a(n+30) from n = 2 on, this sequence consists essentially (except for the initial term) of the apparently unique "loop" of the "PrimeLatz" map A174221. It is used as such in related sequences A293978, ... - M. F. Hasler, Oct 31 2017 LINKS Eric Angelini, The PrimeLatz conjecture E. Angelini, The PrimeLatz Conjecture [Cached copy, with permission] Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1). EXAMPLE 1 is odd;  we add to 1 the next 3 primes (2,3,5) and get 11 11 is odd;  we get 11+(13+17+19)=60 60 is even; we get 30 30 is even; we get 15 15 is odd;  we get 15+(17+19+23)=74 74 is even; we get 37 37 is odd;  we get 37+(41+43+47)=168 168 is even; we get 84 84 is even; we get 42 42 is even; we get 21 21 is odd;  we get 21+(23+29+31)=104 104 is even; we get 52 52 is even; we get 26 26 is even; we get 13 13 is odd;  we get 13+(17+19+23)=72 72 is even; we get 36 36 is even; we get 18 18 is even; we get 9 9 is odd;  we get 9+(11+13+17)=50 50 is even; we get 25 25 is odd;  we get 25+(29+31+37)=122 122 is even; we get 61 61 is odd;  we get 61+(67+71+73)=272 272 is even; we get 136 136 is even; we get 68 68 is even; we get 34 34 is even; we get 17 17 is odd;  we get 17+(19+23+29)=88 88 is even; we get 44 44 is even; we get 22 22 is even; we get 11... thus entering in a loop. ... (from Angelini's web page) MATHEMATICA NestList[If[EvenQ@ #, #/2, Total@ Prepend[NextPrime[#, {1, 2, 3}], #]] &, 1, 101] (* Michael De Vlieger, Oct 25 2017 *) PROG (PARI) vector(100, i, t=if(i>1, A174221(t), 1)) \\ M. F. Hasler, Oct 25 2017 CROSSREFS Cf. A174221, A293980, A293979 (orbit of 83), A293978 (orbit of 443), A293981 (orbit of 209). Sequence in context: A253207 A241860 A082884 * A349120 A077036 A076604 Adjacent sequences:  A193227 A193228 A193229 * A193231 A193232 A193233 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 18 2011 STATUS approved

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Last modified May 27 14:37 EDT 2022. Contains 354105 sequences. (Running on oeis4.)