[seqfan] Re: A113571

[Neil Sloane]

Don, Thanks - I will revise A113571 accordingly
Neil


On Thu, Aug 14, 2014 at 3:27 AM, Don Reble <djr at nk.ca> wrote:

> %I A113571
>> %S 1,2,6,4,10,7,14,8,9,61,22,13,26,1049,41233,16,34,19,38
>> %N Last appearance of n or zero if no such appearance exists.
>> %Y Cf. A110545.
>> %E Sequence continues: a(20)=?, a(21)=?, 23, 46, 138, 50, a(26)=?, 27,
>>    841, 58, 31, 62, 32, 269, 3583, 397, 1297, 74, 199, a(39)=?, 41,
>>    82, 301, 86, 407, 1553, 47, 94, a(48)=?, 98, a(50)=?, 76943, 809,
>>    106, 5953, a(55)=?, a(56)=?, 26693, 59, 118, 2207, ...
>>
>
>    Actually, it's the _first_ appearance of n in A110545.
>
>    One can define this without referring to A110545:
>
>        Let H(n) be the reduced fraction Sum_{i=1..n} 1/i.
>        a(n) is the least factor of H(n)'s numerator or denominator
>        which doesn't divide either part of any earlier H(m).
>
>    so there's a far better way of calculating the sequence, than
>    scanning A110545.
>
>    More terms:
>
> %S A113571 1,2,6,4,10,7,14,8,9,61,22,13,26,1049,41233,16,34,19,38,
> 11167027,
> %T A113571 18858053,23,46,138,50,34395742267,27,841,58,31,62,
> 32,269,3583,397,
> %U A113571 1297,74,199,737281,41,82,301,86,407,1553,47,94,2323031,98,
> 587948341,
>           76943,2809,106,5953,51862596437,252476961434436524654789,
> 26693,59,
>           118,2207,122,928551009361054917576341971,347,64,2473,67,134
>
>    (a(52)=2809, not 809.)
>
>
>  %C Conjectured last occurrence of n:
>>    1,3,11,25,137,49,363,761,7129,7381,83711, [sic] 6617,72072,1117,
>>
>
>    This might be A001008.
>    (That sequence differs after 83711: ...,83711,86021,1145993,1171733,...
>     Maybe the conjecturer scanned A113571, and stopped around a(85000).)
>    But if one of those numerators divides a previous numerator or a
>    previous denominator (A002805), then they're different sequences.
>    Does anyone know whether that happens?
>
> --
> Don Reble  djr at nk.ca
>
>
> --
> This message has been scanned for viruses and
> dangerous content by MailScanner, and is
> believed to be clean.
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com