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

Author

N. J. A. Sloane, Nov 26 2010

Keywords

• nonn

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]

Crossrefs

Bisection gives A174223.

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

Programs

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 *)

PARI

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