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A249742 Inverse permutation to A249741.

%I A249742 #12 Nov 15 2014 16:48:29
%S A249742 1,3,2,6,4,10,7,5,11,15,16,21,22,8,29,28,37,36,46,12,56,45,67,9,79,17,
%T A249742 92,55,106,66,121,23,137,13,154,78,172,30,191,91,211,105,232,38,254,
%U A249742 120,277,14,301,47,326,136,352,18,379,57,407,153,436,171,466,68,497,24,529,190,562,80,596,210,631,231,667,93,704,19
%N A249742 Inverse permutation to A249741.
%H A249742 Antti Karttunen, <a href="/A249742/b249742.txt">Table of n, a(n) for n = 1..8192</a>
%H A249742 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A249742 a(n) = 1 + ((((x+y)^2) - x - 3*y)/2), where x = A055396(n+1) and y = A078898(n+1).
%F A249742 As a composition of related permutations:
%F A249742 a(n) = A249725(A249812(n)).
%F A249742 Other identities.
%F A249742 For all n >= 0 the following holds:
%F A249742 a(A005408(n)) = A000124(n). [Maps odd numbers to central polygonal numbers.]
%F A249742 For all n >= 1 the following holds:
%F A249742 a(A006093(n)) = A000217(n). [Maps precedents of primes to triangular numbers.]
%o A249742 (Scheme) (define (A249742 n) (let ((x (A055396 (+ 1 n))) (y (A078898 (+ 1 n)))) (* (/ 1 2) (- (expt (+ x y) 2) x y y y -2))))
%Y A249742 Inverse: A249741.
%Y A249742 Cf. A000124, A000217, A005408, A006093, A055396, A078898.
%Y A249742 Similar or related permutations: A249725, A249812, A250252.
%Y A249742 Differs from A246276 for the first time at n=20, where a(20) = 12, while A246276(20) = 17.
%K A249742 nonn
%O A249742 1,2
%A A249742 _Antti Karttunen_, Nov 15 2014