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A278801 G.f.: Sum_{k>0} x^prime(k)/(1-x^k). 0
0, 0, 1, 2, 1, 3, 1, 3, 2, 2, 1, 5, 1, 3, 2, 3, 2, 4, 1, 5, 2, 3, 1, 5, 2, 3, 3, 4, 1, 4, 1, 7, 3, 2, 1, 5, 2, 4, 3, 4, 1, 6, 2, 6, 2, 3, 2, 5, 1, 5, 3, 5, 2, 5, 2, 4, 3, 3, 1, 9, 1, 6, 3, 3, 2, 3, 3, 7, 3, 4, 1, 7, 1, 6, 2, 5, 3, 5, 1, 7, 4, 3, 1, 6, 1, 6, 6, 4, 1, 5, 1, 7, 3, 4, 3, 5, 2, 7, 2, 6, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

New maxima occur at 2,3,5,11,31,59,211,331,619,1759,2341,3049,4343,12373,15431,18691,31667,66643,67651,...

4343 and 15431 are the only composites in the terms displayed above.

If we define a new maximum as greater than or equal to the previous maximum we get

1,2,3,5,7,11,19,23,31,59,131,163,167,197,211,331,467,521,547,...

This is very dense with primes and contains the previous list as a subset.

LINKS

Table of n, a(n) for n=0..100.

FORMULA

G.f.: Sum_{k>0} x^prime(k)/(1-x^k).

MATHEMATICA

NN=200; MM=PrimePi[NN]+1; Table[Boole[n>2]+Sum[Boole[(n>Prime[k])&&(Mod[n-Prime[k]+k-1, k] == 0)], {k, 2, MM}], {n, 1, NN}]

CROSSREFS

Sequence in context: A337216 A249617 A304091 * A307720 A191350 A329616

Adjacent sequences:  A278798 A278799 A278800 * A278802 A278803 A278804

KEYWORD

nonn

AUTHOR

Benedict W. J. Irwin, Nov 28 2016

STATUS

approved

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Last modified November 28 16:42 EST 2021. Contains 349413 sequences. (Running on oeis4.)