A242561 a(0)=0; thereafter, a(n) is n multiplied by the distance of a(n-1) to the nearest prime.

0, 2, 0, 6, 4, 5, 0, 14, 8, 9, 20, 11, 0, 26, 42, 15, 32, 17, 0, 38, 20, 21, 44, 23, 0, 50, 78, 27, 56, 87, 60, 31, 0, 66, 34, 105, 72, 37, 0, 78, 40, 41, 0, 86, 132, 45, 92, 141, 96, 49, 100, 51, 104, 53, 0, 110, 56, 171, 116, 177

Offset

0,2

Comments

It appears that any starting value a(0) will produce a sequence which merges with this one at some point.

Also, if we create a new sequence, call it b(n), from this one by changing one term, say a(k), then it appears that there exists an index m such that a(n)=b(n) for all n>=m. For example, if we replace a(10) by 1341, which is a number within the prime gap 1327-1361, then this new sequence has b(17)=a(17) and so the two sequences agree after that point. - J. M. Bergot, May 21 2014.

Links

Table of n, a(n) for n=0..59.

Formula

a(n+1) = n*A051699(a(n)), starting a(0)=0.

Example

The sequence begins with a(0)=0, so |2-0|=2 and a(1)=1*2=2; find
the next m=|2-2|=0, so a(2)=0*2=0; find the next m=|2-0|=2, so a(3)=3*2=6; find the next m=|7-6|=1, so a(4)=1*4=4.

Crossrefs

Sequence in context: A233207 A136656 A256850 * A131595 A290826 A124228

Adjacent sequences: A242558 A242559 A242560 * A242562 A242563 A242564

Keyword

nonn

Author

J. M. Bergot, May 17 2014

Extensions

Edited by N. J. A. Sloane, May 20 2014

Status

approved