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A092193 Number of generations for which prime(n) divides A001008(k) for some k. 4
4, 3, 7, 30, 3, 3, 7, 3, 5, 7, 4, 3, 5, 5, 6, 6, 4, 3, 8, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

For any prime p, generation m consists of the numbers p^(m-1) <= k < p^m. The zeroth generation consists of just the number 0. When there is a k in generation m such that p divides A001008(k), then that k may generate solutions in generation m+1. It is conjectured that for all primes there are solutions for only a finite number of generations. The number of generations is unknown for p=83.

Boyd's table 3 states incorrectly that harmonic primes have 2 generations; harmonic primes have 3 generations.

LINKS

Table of n, a(n) for n=2..22.

David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302.

A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.

EXAMPLE

a(4)=7 because the fourth prime, 7, divides A001008(k) for k = 6, 42, 48, 295, 299, 337, 341, 2096, 2390, 14675, 16731, 16735 and 102728. These values of k fall into 6 generations; adding the zeroth generation makes a total of 7 generations.

CROSSREFS

Cf. A072984 (least k such that prime(n) divides A001008(k)), A092101 (harmonic primes), A092102 (non-harmonic primes).

Sequence in context: A048227 A213661 A176083 * A277117 A155910 A199077

Adjacent sequences:  A092190 A092191 A092192 * A092194 A092195 A092196

KEYWORD

more,nonn

AUTHOR

T. D. Noe, Feb 24 2004; corrected Jul 28 2004

STATUS

approved

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Last modified April 7 01:11 EDT 2020. Contains 333291 sequences. (Running on oeis4.)