A275017 - OEIS

A275017

a(1)=1, a(2)=2, a(n) = prime(n-2) - a(n-2) for n > 2.

1, 2, 1, 1, 4, 6, 7, 7, 10, 12, 13, 17, 18, 20, 23, 23, 24, 30, 35, 31, 32, 40, 41, 39, 42, 50, 55, 51, 48, 56, 61, 57, 66, 74, 71, 65, 78, 86, 79, 77, 88, 96, 91, 85, 100, 108, 97, 91, 114, 132, 113, 97, 120, 142, 121, 109, 136, 154, 133, 117, 144, 164, 139

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

A plot of a(n) vs. n for n = 1..2000 (see the first plot under Links) shows that each of the points apparently falls onto one of four threads that weave back and forth among each other. "Zooming out" to view the first 30000 points results in a plot in which the threads are too close together to be easily distinguishable, but plotting a(n) - 6n vs. n (since all four threads lie fairly near a line of slope 6.0 from n = 0 to about n = 40000) makes it easier to observe the structure of the threads (see the second plot under Links). - Jon E. Schoenfield, Nov 20 2016

The four "threads" correspond a(n) for n in the four congruence classes mod 4. Note that a(n+4)-a(n)=prime(n+2)-prime(n), which might typically be small compared to the differences between a(n),a(n+1),a(n+2) and a(n+3). - Robert Israel, Nov 22 2016

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Jon E. Schoenfield, Plot of a(n) vs. n for n = 1..2000

Jon E. Schoenfield, Plot of a(n) - 6n vs. n for n = 1..30000

MAPLE

A[1]:= 1: A[2]:= 2:

for n from 3 to 1000 do A[n]:= ithprime(n-2)-A[n-2] od:

seq(A[i], i=1..1000); # Robert Israel, Nov 22 2016

MATHEMATICA

a = {1, 2}; Do[AppendTo[a, Prime[n - 2] - a[[n - 2]]], {n, 3, 63}]; a (* Michael De Vlieger, Nov 21 2016 *)

nxt[{n_, a_, b_}]:={n+1, b, Prime[n-1]-a}; NestList[nxt, {2, 1, 2}, 70][[;; , 2]] (* Harvey P. Dale, Aug 18 2024 *)

PROG