A130876: k>1: A130876's dead

[zak seidov]

With including missed terms, A130876 becomes A038550
(see %C A038550),
so A130876'd be dead...
Zak
 
%I A038550
%S A038550
3,5,6,7,10,11,12,13,14,17,19,20,22,23,24,26,28,29,31,34,37,38,40,41,
%T A038550
43,44,46,47,48,52,53,56,58,59,61,62,67,68,71,73,74,76,79,80,82,83,86,
%U A038550
88,89,92,94,96,97,101,103,104,106,107,109,112,113,116,118,122,124,127
%N A038550 Products of an odd prime and a power of two
(sorted).
%C A038550 Numbers that are difference of two
triangular numbers in exactly two ways
%H A038550 T. Verhoeff, <a
href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Rectangular

               and Trapezoidal Arrangements</a>, J.
Integer Sequences, Vol. 2, 1999, 
               #99.1.6.
%Y A038550 Adjacent sequences: A038547 A038548 A038549
this_sequence A038551 A038552 A038553
%Y A038550 Sequence in context: A055597 A053048
A028983 this_sequence A028730 A028747 A073803
%K A038550 nonn
%O A038550 1,1
%A A038550 Tom Verhoeff (Tom.Verhoeff(AT)acm.org)


--- Lekraj Beedassy <boodhiman at yahoo.com> wrote:

> By the way,could someone figure out how this
> sequence A130876 relates to the occurrences of 1 in
> A069283(Number of nontrivial ways to write n as sum
> of at least 2 consecutive integers) ?
>    
>   Lekraj
>    
>   zak seidov <zakseidov at yahoo.com> wrote:
>   Apparently k'd be >1:
> 
> Numbers that can be expressed as the sum of k>1
> consecutive integers in only one way.
> 
> Zak
> 
> 
> %I A130876
> %S A130876
>
5,7,11,12,13,14,17,19,20,22,23,24,26,29,31,34,37,38,40,41,43,44,46,47,
> %T A130876
>
48,52,53,56,58,59,61,62,67,68,71,73,74,76,79,80,82,83,86,88,89,92,94,
> %U A130876
> 96,97,101,103,104,106,107,109,112,113,116,118
> %N A130876 Numbers that can be expressed as the sum
> of
> k consecutive integers in only one way.
> %C A130876 The numbers can be seen as
> sum{i=j..j+k-1}{i}, with j and k integer, being the
> sum of k consecutive integers starting from j.
> %e A130876 37 = 18+19;
> %e A130876 48 = 15+16+17;
> %e A130876 56 = 5+6+7+8+9+10+11;
> %K A130876 easy,nonn,new
> %O A130876 1,1
> %A A130876 Paolo P. Lava & Giorgio Balzarotti
> (ppl(AT)spl.at), Aug 21 2007
> 
> 
> 
> 
>
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Earlier I wrote:
:"Stefan Steinerberger" <stefan.steinerberger at gmail.com> wrote:
::> Is the sequence of positive integers infinite, where m is included in the
::> sequence if and only if: the mth integer from among those positive
::> integers which are coprime to (m+1) = the (m+1)th integer from
::> among those positive integers which are coprime to m ?
::> This sequence begins 3, 15,...
::
::Assuming my programming isn't faulty the sequence should
::go like this: 3, 15, 104, 164, 255, 2625, 2834,...
::So far every number also appears in A001274 although there
::are some numbers (like 194) in A001274 which aren't in the
::sequence.
::
[...]
:It is interesting to see that F_n-2 = 2^(2^n)-1 appears in the sequence
:for n in (1, 2, 3, 4, 5), C(m,m+1) being 2^(2^n+1)-3 in each case.
:F_6, F_7, F_8 and F_9 are not in the sequence, however.

I forgot to mention: I later realised that this occurs precisely when
2^(2^n)-1 is a product of Fermat primes, so there will be no further
examples of this.

Hugo