

A207827


First line of the upper right triangle A207826: Least T[1,n]>0 such that the nth column can be filled with T[k+1,n] = T[k,n1]T[k,n] or T[k,n1]+T[k,n] if the former was used earlier.


2



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
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OFFSET

1,2


COMMENTS

This version differs from the first version A207829, where all possibilities of x+y vs xy 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,n1]T[k,n] and T[k,n1]+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(ab))  return(abs(ab)); !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[k1], lc[k1], setunion( Set( vecextract( nc, 2^(k1)1 )), u )))  next(2))); u=setunion(u, Set(lc=nc)); show & print1(nc[1]", "); nc[1])}


CROSSREFS

Sequence in context: A047540 A116478 A207829 * A047236 A039581 A338420
Adjacent sequences: A207824 A207825 A207826 * A207828 A207829 A207830


KEYWORD

nonn


AUTHOR

M. F. Hasler, Feb 20 2012


STATUS

approved



