Sequences that pass recursion test, but ...

Sat Mar 3 03:13:57 CET 2007

sum of prime divisors of n is ≥ n.
 >
 > Something wrong with A088475. Why 10 is an element of A088475?
 > 10 has two prime divisors: 2 and 5. Their dismal sum is 5 (according
 > to the definition given in A087061) which is less than 10. What's
 > wrong?
   ...dismal sum of *dismal* prime divisors...
 > btw, I think dismal-related sequences are missing the "base" keyword
 > as the dismal operation are defined via decimal representations of the
 > operands.
structure.  So B=10 is kind of an exemplar of the more typical cases, 
Return-Path: <njas at research.att.com>
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From: "N. J. A. Sloane" <njas at research.att.com>
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To: seqfan at ext.jussieu.fr, Marc LeBrun <mlb at well.com>
Subject: Re: Sequences that pass recursion test, but ...
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Is it worth submitting a table associated with A126086?:

Table, by rows, T(n,k) = Number of paths of length k from (0,0,0) to
(n,n,n) such that at each step (i) at least one coordinate increases,
(ii) no coordinate decreases, (iii) no coordinate increases by more
than 1, and (iv) all coordinates are integers.

Table begins:
1, 6, 6, 1, ...

Example: since
%e A126086 Illustrating a(1) = 13:
%e A126086 000 -> 001 -> 011 -> 111
%e A126086 000 -> 001 -> 101 -> 111
%e A126086 000 -> 001 -> 111
%e A126086 000 -> 010 -> 011 -> 111
%e A126086 000 -> 010 -> 110 -> 111
%e A126086 000 -> 010 -> 111
%e A126086 000 -> 100 -> 101 -> 111
%e A126086 000 -> 100 -> 110 -> 111
%e A126086 000 -> 100 -> 111
%e A126086 000 -> 011 -> 111
%e A126086 000 -> 101 -> 111
%e A126086 000 -> 110 -> 111
%e A126086 000 -> 111
a(1,1) = 1   {000 -> 111}
a(1,2) = 6 {000 -> 001 -> 111, 000 -> 010 -> 111, 000 -> 010 -> 111,
000 -> 011 -> 111, 000 -> 101 -> 111, 000 -> 110 -> 111}
a(1,3) = 6 {000 -> 001 -> 011 -> 111, 000 -> 001 -> 101 -> 111, 000 ->
010 -> 110 -> 111, 000 -> 100 -> 101 -> 111, 000 -> 100 -> 110 -> 111}

Row sums of n-th are A126086(n).

Hello all,

With the corrected definition of A088475 (Numbers n such that dismal sum of the dismal prime divisors of n is >= n) can someone comment on the fact that it looks like arithmetic progression.

You should also correct this:
A088480 Numbers n such that dismal product of prime divisors of n is >= n.

Tanya

---------- Original Message ----------------------------------

>New version:
>
>%I A088475
>%S A088475 10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
>%T A088475 32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
>%U A088475 54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75
>%N A088475 Numbers n such that dismal sum of the dismal prime divisors of n is >= n.
>%e A088475 The only dismal prime that divides 10 is 90: 90*1 = 10 (cf. A087061, A087062, A08\
>7097), and 90+1 = 91 >= 10, so 10 is a member. - njas, Mar 04 2007
>%H A088475 D. Applegate, <a href="http://www.research.att.com/~njas/sequences/a087061.txt">C\
> program for dismal arithmetic and number theory</a>
>%H A088475 <a href="http://www.research.att.com/~njas/sequences/Sindx_Di.html#dismal">Index \
>entries for sequences related to dismal arithmetic</a>
>%Y A088475 Sequence in context: A063671 A123895 A100830 this_sequence A001637 A102494 A11788\
>4
>%Y A088475 Adjacent sequences: A088472 A088473 A088474 this_sequence A088476 A088477 A088478
>%K A088475 nonn,base
>%O A088475 1,1
>%A A088475 David Applegate (david(AT)research.att.com), Nov 11 2003
>%E A088475 Definition made more precise by Marc LeBrun, Mar 04 2007
>
>Neil
>

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