A140609 - OEIS

%I #4 Jan 08 2013 10:09:55

%S 17,25,31,32,36,43,45,46,50,51,53,59,60,62,63,66,67,68,69,74,78,79,81,

%T 83,86,87,88,92,93,95,98

%N Numbers never equal to the number of partitions of any p into k parts (2<k<=n).

%C a(n) is the least number greater than a(n-1) which never occurs in the sequence S(p,q) {p;0;infinity}{k;3;p).

%C Any number q appears twice for k =2 as S(2*q,2) and S(2*q+1,2)

%C For k >2 the smallest values of natural numbers appear for first time as follows for increasing p:

%C 1=S(3,3)

%C 2=S(5,3)

%C 3=S(6,3)

%C 4=S(7,3)

%C 5=S(8,3)

%C 6=S(9,4)

%C 7=S(9,3)

%C 8=S(10,3)

%C 9=S(10,4)

%C 10=S(11,3)

%C 11=S(11,4)

%C 12=S(12,3)

%C 13=S(12,5)

%C 14=S(13,3)

%C 15=S(12,4)

%C 16=S(14,3)

%C 18=S(13,4)

%C 17 never occurs, hence a(1) = 17

%Y Cf. A000041; A002865.

%K easy,nonn

%O 1,1

%A Philippe Lallouet (philip.lallouet(AT)orange.fr), May 18 2008