A250470 a(n) = A249817(A064989(A249818(n))).

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

Offset

1,3

Comments

Odd bisection, A250472, is a permutation of natural numbers. A250479 gives the even bisection.

For odd numbers n >= 3, a(n) = A078898(n)-th number k for which A055396(k) = A055396(n)-1. In other words, a(n) tells which number is located immediately above n in the sieve of Eratosthenes (see A083140, 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 injection A250469.]

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

Prog

(Scheme) (define (A250470 n) (A249817 (A064989 (A249818 n))))

Crossrefs

Cf. A055396, A064989, A078898, A083140, A083221, A249744, A249810, A249820, A249817, A249818, A250469.

Odd bisection: A250472.

Even bisection: A250479.

Differs from A064989 for the first time at n=21, where a(21) = 8, while

A064989(21) = 10.

Sequence in context: A169747 A269380 A268674 * A064989 A290099 A250479

Adjacent sequences: A250467 A250468 A250469 * A250471 A250472 A250473

Keyword

nonn

Author

Antti Karttunen, Dec 06 2014

Status

approved