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A008348 a(0)=0; thereafter a(n) = a(n-1) + prime(n) if a(n-1) < prime(n), otherwise a(n) = a(n-1) - prime(n). 15
0, 2, 5, 0, 7, 18, 5, 22, 3, 26, 55, 24, 61, 20, 63, 16, 69, 10, 71, 4, 75, 2, 81, 164, 75, 172, 71, 174, 67, 176, 63, 190, 59, 196, 57, 206, 55, 212, 49, 216, 43, 222, 41, 232, 39, 236, 37, 248, 25, 252, 23, 256, 17, 258, 7, 264, 1, 270, 541, 264, 545, 262, 555 (list; graph; refs; listen; history; text; internal format)
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 counter-example 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 *)

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

Cf. A008344, A022831, A022837, A309225.

Sequence in context: A096319 A146105 A022832 * A201576 A265299 A020836

Adjacent sequences:  A008345 A008346 A008347 * A008349 A008350 A008351

KEYWORD

nonn,look

AUTHOR

N. J. A. Sloane and J. H. Conway

EXTENSIONS

More terms from Clark Kimberling

Name edited by Dmitry Kamenetsky, Feb 14 2017

STATUS

approved

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)