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%I #19 Aug 01 2021 12:58:17
%S 1,3,4,6,13,7,9,18,10,12,28,15,25,63,16,19,33,39,21,43,22,24,88,27,61,
%T 48,30,46,58,31,34,138,60,36,73,37,40,123,72,42,313,45,67,78,49,94,93,
%U 81,51,163,52,54,193,55,57,103,64,102,213,105,85,108,172,66,118,69,127,438,70,75,133,111,109,303
%N Odd bisection of A048673: a(n) = A048673(2*n-1).
%C Shift the prime factorization of odd numbers one step towards larger primes, add one and divide by two.
%F a(n) = A048673(2*n-1) = (1+A003961(2*n-1)) / 2 = (1+A249735(n)) / 2.
%F a(n) = A032766(A249746(n)).
%e For n = 8, the eighth odd number is 2*8 - 1 = 15 = 3*5 = prime(2) * prime(3). By adding one to both prime indices, we get prime(3) * prime(4) = 5*7 = 35, and (35+1)/2 = 18, thus a(8) = 18. Here prime(n) = A000040(n).
%o (Scheme, two versions)
%o (define (A254049 n) (A048673 (+ n n -1)))
%o (define (A254049 n) (/ (+ 1 (A003961 (+ n n -1))) 2))
%Y Cf. A032766 (omitting the initial 0, the same sequence sorted into ascending order).
%Y Also a permutation of A253888.
%Y Cf. A000040, A003961, A048673, A249735, A249746, A254050, A254051, A254053.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 24 2015
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