Rép. : RE: Bernoulli numbers and arithmetic progressions

[Mohammed BOUAYOUN]

Cher N.J.A. Sloane
je vient de découvrir une relation tres interessante

indice                     ratio
1         574             37
2         1185
3         1240           37
4         1269
5         1376
6         1906           37
7         1910
8         2572           37
9         2689
10       2980
11       3238           37

quand ratio = 37 on'a la suite 1,3,6,8,11,14,16,19 qui 'est tout simplement A026352

cordialement

Mohammed Bouayoun


>>> "N. J. A. Sloane" <njas at research.att.com> 02/05 4:09  >>>
i believe (and have suggested to the list)
that Kummer's Congruence explains the answer

the simplest way to see the question
is to look at sequences A090496 A090495 which are
based on the surprising fact that A001067 and A046968
agree for the first 574 or so terms but then differ

it is also clear i think that the terms of A090496
are products of irregular primes, although so far only single
primes have shown up

Neil

JHC wrote:
    What is the conjecture being spoken of here?  It sounds as though it's
some kind of congruence involving Bernoulli numbers, in which case I'd 
like to have a shot at it.
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