A249815 Permutation of natural numbers: a(n) = A249741(A055396(n+1), A246277(n+1)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 26, 21, 22, 23, 24, 25, 20, 27, 28, 29, 30, 31, 38, 33, 34, 35, 36, 37, 62, 39, 40, 41, 42, 43, 32, 45, 46, 47, 48, 49, 74, 51, 52, 53, 64, 55, 98, 57, 58, 59, 60, 61, 56, 63, 94, 65, 66, 67, 110, 69, 70, 71, 72, 73, 50, 75, 76, 77, 78, 79, 44, 81, 82, 83

Offset: 1

Author

Antti Karttunen, Nov 06 2014

Keywords

• nonn

Comments

a(n) tells which number in square array A249741 (the sieve of Eratosthenes minus 1) is at the same position where n is in array A246275. As the topmost row in both arrays is A005408 (odd numbers), they are fixed, i.e. a(2n+1) = 2n+1 for all n. Also, as the leftmost column in both arrays is primes minus one (A006093), they are also among the fixed points.

Equally: a(n) tells which number in array A114881 is at the same position where n is in the array A246273, as they are the transposes of above two arrays.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A249816

Similar or related permutations: A250244 ("deep variant"), A246675, A249811, A249817, A246273, A246275, A114881, A249741.

Cf. A005408, A006093, A055396, A246277.

Differs from A249816 and A250243 for the first time at n=32, where a(32) = 38, while A249816(32) = A250243(32) = 44.

Differs from A250244 for the first time at n=39, where a(39) = 39, while A250244(39) = 51.

Programs

Scheme

(define (A249815 n) (+ -1 (A083221bi (A246277 (+ 1 n)) (A055396 (+ 1 n))))) ;; Code for A083221bi given in A083221

Formula

a(n) = A249741(A055396(n+1), A246277(n+1)).

As a composition of other permutations:

a(n) = A249811(A246675(n)).

a(n) = A249817(n+1) - 1.

Other identities. For all n >= 1:

a(A005408(n-1)) = A005408(n-1) and a(A006093(n)) = A006093(n). [Fixes odd numbers and precedents of primes. Cf. comments above].