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.

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

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, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C program for A285884

Rémy Sigrist, Density plot of the first 2500000 terms

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

Cf. A002858, A068799, A033629, A287611.

Sequence in context: A242289 A349229 A158515 * A123709 A165482 A323242

Adjacent sequences: A285881 A285882 A285883 * A285885 A285886 A285887

Keyword

nonn

Author

Enrique Navarrete, Apr 27 2017

Status

approved