

A242561


a(0)=0; thereafter, a(n) is n multiplied by the distance of a(n1) to the nearest prime.


0



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
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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 13271361, 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



FORMULA

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


EXAMPLE

The sequence begins with a(0)=0, so 20=2 and a(1)=1*2=2; find
the next m=22=0, so a(2)=0*2=0; find the next m=20=2, so a(3)=3*2=6; find the next m=76=1, so a(4)=1*4=4.


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



