A348413 a(0) = A002858(1) = 1, followed by the greatest Ulam numbers A002858 to form a complete sequence (see algorithm below).

1, 2, 4, 8, 16, 28, 57, 114, 221, 451, 893, 1792, 3549, 7104, 14212, 28445, 56894, 113792, 227554, 455124, 910208, 1820449, 3640907, 7281813, 14563613, 29127251, 58254501, 116508984, 233017889, 466035877, 932071736

Offset

0,2

Comments

This sequence starts at a(0)=1, subsequent terms a(n) for n>0 being obtained by selecting the (greatest Ulam number) <= 1+Sum_{i=0..n-1} a(i). This ensures that the sequence is complete because Sum_{i=0..n-1} a(i) >= a(n)-1, for all n>=0 and a(0)=1, is a necessary and sufficient condition for completeness.

Links

Table of n, a(n) for n=0..30.

Wikipedia, Ulam number.

Formula

a(n) = (greatest Ulam number) <= 1+Sum_{i=0..n-1} a(i), with a(0) = 1.

Example

Given that the first 7 terms of the sequence are 1, 2, ..., 28, 57 then a(7)=(greatest Ulam number) <= (1+2+...+28, 57) + 1 = 117, hence a(7)=114.

Mathematica

lst1 = Last/@ReadList["https://oeis.org/A002858/b002858.txt", {Number, Number}]; lst={1, 2}; n=3; Do[s=Total@lst; While[s+1>=lst1[[n]], n++]; AppendTo[lst, lst1[[n-1]]], 16]; lst

Crossrefs

Cf. A002858.

Sequence in context: A255937 A357763 A330289 * A355968 A177269 A018726

Adjacent sequences: A348410 A348411 A348412 * A348414 A348415 A348416

Keyword

nonn,more

Author

Frank M Jackson, Oct 17 2021

Extensions

a(18)-a(30) from Amiram Eldar, Oct 17 2021

Status

approved