A128983 - OEIS

%I #3 Mar 30 2012 17:39:19

%S 0,1,2,0,4,0,8,6,9,10,16,12,32,18,33,34,64,36,128,66,129,130,256,132,

%T 257,258,134,260,512,264,1024,514,1025,1026,268,1028,2048,1032,2049,

%U 2050,4096

%N Rightmost position of n in A089625, 0 if absent.

%C Numbers n have A000586(n) decompositions into sums of distinct primes and occur A000586(n) times in A089625. The sequence is the rightmost (largest) index (position) of n in A089625. It is an inverse of A089625 made unique in the sense that in the prime decomposition of n the one with the largest primes are chosen and converted to binary. The sequence therefore is a binary representation of a greedy decomposition of n into a sum of primes.

%F A089625(a(n))=n if n not equal to 1, 4 and 6.

%e Prime decompositions of n=25 are 1*11+1*7+1*5+0*3+1*2 (binary tagged 11101=29)

%e or 1*13+0*11+1*7+0*5+1*3+1*2 (binary 101011=43) or

%e 1*13+0*11+1*7+1*5+0*3+0*2 (binary 101100=44) or 1*17+0*13+0*11+0*7+1*5+1*3+0*2

%e (binary 1000110=70) or 1*23+0*19+0*17+0*13+0*11+0*7+0*5+0*3+1*2 (binary 100000001

%e =257). Out of these indices 29, 43, 44, 70 and 257, the largest is chosen, a(25)=257.

%Y Cf. A089625, A000586.

%K nonn

%O 1,3

%A _R. J. Mathar_, Apr 30 2007