A128983 - OEIS

A128983

Rightmost position of n in A089625, 0 if absent.

0, 1, 2, 0, 4, 0, 8, 6, 9, 10, 16, 12, 32, 18, 33, 34, 64, 36, 128, 66, 129, 130, 256, 132, 257, 258, 134, 260, 512, 264, 1024, 514, 1025, 1026, 268, 1028, 2048, 1032, 2049, 2050, 4096

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OFFSET

1,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..41.

FORMULA

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

EXAMPLE

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

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

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

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

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

CROSSREFS

Cf. A089625, A000586.