A249815 - OEIS

%I #17 Nov 17 2014 22:02:07

%S 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,

%T 27,28,29,30,31,38,33,34,35,36,37,62,39,40,41,42,43,32,45,46,47,48,49,

%U 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

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

%C 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.

%C 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.

%H Antti Karttunen, <a href="/A249815/b249815.txt">Table of n, a(n) for n = 1..8192</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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

%F As a composition of other permutations:

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

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

%F Other identities. For all n >= 1:

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

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

%Y Inverse: A249816

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

%Y Cf. A005408, A006093, A055396, A246277.

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

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 06 2014