A250470 - OEIS

A250470

1, 1, 2, 1, 3, 2, 5, 1, 4, 3, 7, 2, 11, 5, 6, 1, 13, 4, 17, 3, 8, 7, 19, 2, 9, 11, 10, 5, 23, 6, 29, 1, 12, 13, 15, 4, 31, 17, 14, 3, 37, 10, 41, 7, 16, 19, 43, 2, 25, 9, 18, 11, 47, 8, 21, 5, 20, 23, 53, 6, 59, 29, 22, 1, 27, 14, 61, 13, 24, 15, 67, 4, 71, 31, 26, 17, 35, 22, 73, 3, 28, 37, 79, 10, 33, 41, 30, 7, 83, 12, 55, 19, 32, 43, 39, 2, 89, 25, 34, 9, 97, 26, 101

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OFFSET

1,3

COMMENTS

Odd bisection,A250472,is a permutation of natural numbers.A250479gives the even bisection.

For odd numbers n >= 3, a(n) =A078898(n)-th number k for whichA055396(k) =A055396(n)-1. In other words, a(n) tells which number is located immediately above n in the sieve of Eratosthenes (seeA083140,A083221) in the same column of the sieve that contains n.

LINKS

Antti Karttunen,Table of n, a(n) for n = 1..9048

FORMULA

a(n) =A249817(A064989(A249818(n))).

Other identities. For all n >= 1:

a(A250469(n)) = n. [This is an inverse function for injectionA250469.]

For all odd numbers n >= 3:A055396(a(n)) =A055396(n)-1.

PROG

(Scheme) (define (A250470n) (A249817(A064989(A249818n))))

CROSSREFS