OFFSET
0,2
COMMENTS
a(n) < 2*prime(n). Conjecture: a(n) > 0 for n > 3. - Thomas Ordowski, Dec 03 2016 [This conjecture is false, because a(369019)=0. The next counterexample occurs at n = 22877145. - Dmitry Kamenetsky, Feb 14 2017. (Cf. A309225.)]
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = c(1)p(1) + ... + c(n)p(n), where c(i) = 1 if a(i-1) > p(i) and c(i) = -1 if a(i-1) <= p(i) (p(i) = primes). - Clark Kimberling
MAPLE
A008348 := proc(n) option remember; if n = 0 then 0 elif A008348(n-1)>=ithprime(n) then A008348(n-1)-ithprime(n); else A008348(n-1)+ithprime(n); fi; end;
# Maple from N. J. A. Sloane, Aug 31 2019 (Start)
# Riecaman transform
Riecaman := proc(a, s, M)
# Start with s, add or subtract a[n], get M terms. If a has w terms, can get M=w+1 terms.
local b, M2, n, t;
if whattype(a) <> list then ERROR("First argument should be a list"); fi;
if a[1]=0 then ERROR("a[1] should not be zero"); fi;
M2 := min(nops(a), M-1);
b:=[s]; t:=s;
for n from 1 to M2 do
if a[n]>t then t:=t+a[n] else t:=t-a[n]; fi; b:=[op(b), t]; od:
b; end;
# Riecaman transform of primes, starting at s=0
p1:=[seq(ithprime(i), i=1..100)];
q0:=Riecaman(p1, 0, 99);
# End
MATHEMATICA
a := {0}; For[n = 2, n < 100, n++, If[a[[n - 1]] >= Prime[n - 1], b := a[[n - 1]] - Prime[n - 1], b := a[[n - 1]] + Prime[n - 1]; ]; a = Append[a, b]]; a (* Stefan Steinerberger, May 02 2006 *)
nxt[{n_, a_}]:={n+1, If[a<Prime[n+1], a+Prime[n+1], a-Prime[n+1]]}; NestList[nxt, {0, 0}, 70][[;; , 2]] (* Harvey P. Dale, Sep 13 2024 *)
PROG
(PARI) lista(nn) = {print1(a=0, ", "); for (n=1, nn, if (a < (p=prime(n)), a += p, a -= p); print1(a, ", "); ); } \\ Michel Marcus, Dec 04 2016
CROSSREFS
KEYWORD
nonn,look
AUTHOR
EXTENSIONS
More terms from Clark Kimberling
Name edited by Dmitry Kamenetsky, Feb 14 2017
STATUS
approved