A174221 a(n) = n/2 if n is even, otherwise add to n the next three primes > n.

0, 11, 1, 26, 2, 36, 3, 48, 4, 50, 5, 60, 6, 72, 7, 74, 8, 88, 9, 102, 10, 104, 11, 120, 12, 122, 13, 124, 14, 138, 15, 152, 16, 154, 17, 156, 18, 168, 19, 170, 20, 184, 21, 202, 22, 204, 23, 220, 24, 222, 25, 224, 26, 240, 27, 242, 28, 244, 29, 258, 30, 272, 31, 274, 32, 276, 33, 290, 34, 292, 35, 306, 36, 324, 37, 326, 38, 328, 39, 348, 40, 350, 41, 370, 42

Offset

0,2

Comments

Related to the PrimeLatz conjecture, which states that if this map k -> a(k) is iterated, starting at any n >= 0, then the trajectory will eventually enter a loop.

Computations have shown that up to 10^8, there is only one loop (apart from the fixed point 0). It is given for example by terms 2 through 31 of A193230, the smallest of its 30 elements being 9.

See A293980 for the number of iterations required to reach an element of this loop, and for further study of trajectories under iterations of this map.

References

Eric Angelini, Posting to Math Fun Mailing List, Nov 26, 2010

Bill Thurston, Posting to Math Fun Mailing List, Nov 26, 2010

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

E. Angelini, The PrimeLatz Conjecture [Cached copy, with permission]

Maple

f:=proc(n) local p; p:=nextprime;
if n mod 2 = 0 then n/2 else
n+p(n)+p(p(n))+p(p(p(n))); fi; end;

Mathematica

Array[If[EvenQ@ #, #/2, Total@ Prepend[NextPrime[#, {1, 2, 3}], #]] &, 85, 0] (* Michael De Vlieger, Oct 25 2017 *)

Prog

(PARI) A174221(n)=bittest(n, 0)||return(n\2); n+sum(c=1, 3, n=nextprime(n+1)) \\ M. F. Hasler, Oct 25 2017

Crossrefs

Bisection gives A174223.

Cf. A193230 (trajectory of 1 under this map), A293979 (trajectory of 83), A293980.

Sequence in context: A282868 A013618 A014467 * A194039 A298084 A275304

Adjacent sequences: A174218 A174219 A174220 * A174222 A174223 A174224

Keyword

nonn

Author

N. J. A. Sloane, Nov 26 2010

Status

approved