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

Author

J. M. Bergot, May 17 2014

Keywords

• nonn

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.

Examples

			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.
		

Formula

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

Extensions

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