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A282846 Start with a(0) = 0, c = 1, p = 2. Thereafter, if a(n) < c, then a(n+1) = a(n) + p and p is set to the next larger prime; else, a(n+1) = a(n) - c and c is set to the next larger composite number. 7
0, 2, 1, 4, 0, 5, 12, 6, 17, 9, 0, 13, 3, 20, 8, 27, 13, 36, 21, 5, 34, 16, 47, 27, 6, 43, 21, 62, 38, 13, 56, 30, 3, 50, 22, 75, 45, 13, 72, 39, 5, 66, 31, 98, 62, 24, 95, 56, 16, 89, 47, 3, 82, 37, 120, 74, 26, 115, 66, 16, 113, 62, 10, 111, 57, 2, 105, 49, 156, 99, 41, 150, 90, 28, 141, 78, 14, 141, 76, 10, 141, 73, 4, 141, 71, 210, 138, 64, 213 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First differences are primes and negative nonprimes; their absolute values yield a permutation of the positive integers.

See A282864 for the permutation of the nonnegative integers corresponding to the order in which the numbers are used in this sequence.

LINKS

M. F. Hasler, Table of n, a(n) for n = 0..10000 (a(0..5000) from Jean-Marc Falcoz.)

E. Angelini, Le restaurant new-yorkais, February 2017

MAPLE

P:=proc(q) local a, c, n, p; a:=0; c:=1; p:=2; print(a); for n from 1 to q do

if a<c then a:=a+p; p:=nextprime(p); else a:=a-c; c:=c+1; while isprime(c) do c:=c+1; od; fi;

print(a); od; end: P(10^2); # Paolo P. Lava, Feb 23 2017

PROG

(PARI) A282846(n, s=0, a=0, c=1, p=2)={for(n=1, n, s&&print1(a", "); if(a<c, a+=p; p=nextprime(p+1), a-=c; while(isprime(c++), ))); a} \\ Set 2nd argument s to 1 to print all intermediate terms.

CROSSREFS

Cf. A282864

Sequence in context: A087664 A158032 A282886 * A326129 A326144 A120112

Adjacent sequences:  A282843 A282844 A282845 * A282847 A282848 A282849

KEYWORD

nonn,look

AUTHOR

Eric Angelini, Jean-Marc Falcoz and M. F. Hasler, Feb 22 2017

STATUS

approved

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Last modified April 4 08:58 EDT 2020. Contains 333213 sequences. (Running on oeis4.)