Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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