A207827 First line of the upper right triangle A207826: Least T[1,n]>0 such that the n-th column can be filled with T[k+1,n] = |T[k,n-1]-T[k,n]| or T[k,n-1]+T[k,n] if the former was used earlier.

1, 2, 4, 7, 8, 10, 13, 12, 16, 20, 19, 32, 24, 34, 29, 40, 31, 45, 52, 42, 62, 81, 46, 47, 91, 68, 111, 70, 84, 99, 61, 113, 80, 78, 125, 85, 141, 105, 102, 130, 55, 106, 142, 168, 98, 188, 135, 120, 189, 150, 157, 295, 171, 195, 178, 254, 164, 216, 212, 144

Offset

1,2

Comments

This version differs from the first version A207829, where all possibilities of x+y vs |x-y| are tested in a given column, before discarding a candidate for the next element of the first line. Here a candidate a(n)=T[1,n] is discarded when successive ("greedy") choices of smallest possible elements T[k,n] (k=2, 3,...) lead (in some subsequent row k) to a situation where no choice is possible, i.e., both |T[k,n-1]-T[k,n]| and T[k,n-1]+T[k,n] appear earlier.

Links

Table of n, a(n) for n=1..60.

E. Angelini, Tableau avec soustractions/additions, Feb 19 2012

E. Angelini, Tableau avec soustractions/additions [Cached copy, with permission]

Prog

(PARI) list_A207827(Nmax, show=1/*print out terms as they are calculated*/)={ my( u=[], lc=u, f(a, b, u) = setsearch( u, abs(a-b)) || return(abs(a-b)); !setsearch( u, a+b ) & return(a+b)); vector( Nmax, n, my(nc=vector(n)); until( nc[n], while( setsearch( u, nc[1]++), ); for( k=2, n, (nc[k] = f( nc[k-1], lc[k-1], setunion( Set( vecextract( nc, 2^(k-1)-1 )), u ))) || next(2))); u=setunion(u, Set(lc=nc)); show & print1(nc[1]", "); nc[1])}

Crossrefs

Sequence in context: A047540 A116478 A207829 * A047236 A371638 A039581

Adjacent sequences: A207824 A207825 A207826 * A207828 A207829 A207830

Keyword

nonn

Author

M. F. Hasler, Feb 20 2012

Status

approved