Search: id:A111774
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%I A111774
%S A111774 6,9,10,12,14,15,18,20,21,22,24,25,26,27,28,30,33,34,35,36,38,39,40,42,
%T A111774 44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,65,66,68,69,70,72,74,
%U A111774 75,76,77,78,80,81,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100,102
%N A111774 Numbers that can be written as a sum of at least three consecutive positive 
               integers.
%C A111774 In this sequence there are no (odd) primes and there are no powers of 
               2.
%C A111774 So we have only three kinds of natural numbers: the odd primes, the powers 
               of 2 and the numbers that can be represented as a sum of at least 
               three consecutive integers.
%C A111774 Odd primes can only be written as a sum of two consecutive integers. 
               Powers of 2 do not have a representation as a sum of k consecutive 
               integers (other than the trivial n=n, for k=1).
%C A111774 See also A066542, conjectured complementary (in a way) to this sequence 
               (Jon Awbrey, Aug 15 2005)
%D A111774 Nieuw Archief voor Wiskunde 5/6 nr. 2 Problems/UWC, Problem C, Jun 2005, 
               p. 181-182
%H A111774 Nieuw Archief voor Wiskunde 5/6 nr. 2 Problems/UWC, Problem C: <a href="http:/
               /www.jaapspies.nl/mathfiles/problem2005-2C.pdf">solution of this 
               Problem</a>
%H A111774 J. Spies, <a href="http://www.jaapspies.nl/oeis/a111774.sage">SAGE program 
               for computing A111774</a>
%e A111774 a(1)=6 because 6 is the first number that can be written as a sum of 
               three consecutive positive integers: 6 = 1+2+3.
%p A111774 ispoweroftwo := proc(n) local a, t; t := 1; while (n > t) do t := 2*t 
               end do; if (n = t) then a := true else a := false end if; return 
               a; end proc; f:= proc(n) if (not isprime(n)) and (not ispoweroftwo(n)) 
               then return n end if; end proc; seq(f(i),i = 1..150);
%Y A111774 Cf. A000040, A000079, A066542.
%Y A111774 Sequence in context: A103092 A104523 A091886 this_sequence A036347 A129492 
               A053869
%Y A111774 Adjacent sequences: A111771 A111772 A111773 this_sequence A111775 A111776 
               A111777
%K A111774 easy,nonn
%O A111774 1,1
%A A111774 Jaap Spies (j.spies(AT)hccnet.nl), Aug 15 2005

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