A249816 - OEIS

%I #15 Nov 17 2014 22:02:16

%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 27,28,29,30,31,44,33,34,35,36,37,32,39,40,41,42,43,80,45,46,47,48,49,

%U 74,51,52,53,124,55,62,57,58,59,60,61,38,63,54,65,66,67,134,69,70,71,72,73,50,75,76,77,78,79,98,81,82,83

%N Permutation of natural numbers: a(n) = A246275(A055396(n+1), A078898(n+1)).

%C a(n) tells which number in square array A246275 is at the same position where n is in array A249741, the sieve of Eratosthenes minus 1. 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 A246273 is at the same position where n is in the array A114881, as they are the transposes of above two arrays.

%H Antti Karttunen, <a href="/A249816/b249816.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A246275(A055396(n+1), A078898(n+1)).

%F As a composition of other permutations:

%F a(n) = A246676(A249812(n)).

%F a(n) = A249818(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 (A249816 n) (+ -1 (A246278bi (A055396 (+ 1 n)) (A078898 (+ 1 n)))))

%Y Inverse: A249815.

%Y Cf. A005408, A006093, A055396, A078898, A246278.

%Y Similar or related permutations: A250243 ("deep variant"), A246676, A249812, A249818, A246273, A246275, A114881, A249741.

%Y Differs from A249815 and A250244 for the first time at n=32, where a(32) = 44, while A249815(32) = A250244(32) = 38.

%Y Differs from A250244 for the first time at n=39, where a(39) = 39, while A250243(39) = 51.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 06 2014