The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 27 22:47 EDT 2023. Contains 361575 sequences. (Running on oeis4.)