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A285884 For n => 1, the number of distinct summands u and v that can be used in the representation of n as u+v, where u and v are two (possibly equal) Ulam numbers A002858. 2
0, 1, 2, 3, 4, 3, 4, 3, 4, 4, 2, 5, 2, 6, 4, 3, 6, 2, 8, 4, 4, 5, 0, 6, 0, 3, 4, 2, 8, 4, 4, 5, 0, 6, 0, 3, 4, 2, 8, 4, 4, 6, 0, 8, 0, 4, 2, 2, 8, 4, 6, 5, 2, 10, 4, 7, 2, 4, 6, 4, 6, 2, 6, 10, 6, 8, 0, 4, 2, 6, 4, 3, 10, 6, 10, 5, 2, 6, 4, 8, 4, 2, 10, 4, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
An odd number in the sequence means that there exists the "pseudo-representation" u + u, where u is an Ulam number. For example, a(22)=5 since 22 = 18 + 4 = 16 + 6 = 11 + 11, and the 5 distinct summands 18,4,16,6,11 are Ulam numbers.
Note that both 2 and 3 are values for Ulam numbers since, by the previous comment, a value of 3 means that the Ulam number has the additional "pseudo-representation" u + u (see the Examples).
It seems that all nonnegative integers occur as values of this sequence.
LINKS
Rémy Sigrist, C program for A285884
EXAMPLE
a(23) = 0 since 23 can't be written as the sum of two distinct Ulam numbers. This type of numbers are in A033629.
a(94) = 1 since 94 = 47 + 47, where 47 is an Ulam number. This type of numbers are in A287611.
a(11) = 2 since 11 has the unique representation 11 = 8 + 3, where 8,3 are Ulam numbers. If such n is also an Ulam number (such as 11), then it is in A002858.
a(8) = 3 since it has the representation 8 = 6 + 2 and also the additional "pseudo-representation" 8 = 4 + 4, where 6, 2, and 4 are Ulam numbers. If n has such a "pseudo-representation" and is an Ulam number, then it is in A068799.
PROG
(C) See Links section.
CROSSREFS
Sequence in context: A242289 A349229 A158515 * A123709 A165482 A323242
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Apr 27 2017
STATUS
approved

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Last modified May 30 06:59 EDT 2024. Contains 372962 sequences. (Running on oeis4.)