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%I #13 Aug 17 2022 03:11:06
%S 3,45,91,209,375,493,735,897,1215,1581,1815,2257,2747,3053,3619,3969,
%T 4611,5301,5723,6489,6955,7797,8687,9225,10191,11205,11815,12905,
%U 13559,14725,15939,16665,17955,19293,20091,21505,22347,23837,25375,26289
%N Pair the odd numbers such that the k-th pair is (r, r+2k) where r is the smallest odd number not included earlier: (1, 3), (5, 9), (7, 13), (11, 19), (15, 25), (17, 29), (21, 35), (23, 39), (27, 45), ... This is the sequence of the product of the members of pairs.
%F a(n) = A075317(n)*A075318(n). - _R. J. Mathar_, Nov 12 2006
%p A075320 := proc(nmax) local r,k,a,pairs ; a := [3] ; pairs := [1,3] ; k := 2 ; r := 5 ; while nops(a) < nmax do while r in pairs do r := r+2 ; od ; if r+2*k in pairs then printf("inconsistency",k) ; fi ; a := [op(a),r*(r+2*k)] ; pairs := [op(pairs),r,r+2*k] ; k := k+1 ; od ; RETURN(a) ; end: a := A075320(200) : for n from 1 to nops(a) do printf("%d,",op(n,a)) ; od ; # _R. J. Mathar_, Nov 12 2006
%o (Python)
%o from math import isqrt
%o def A075320(n): return (m:=(n+isqrt(5*n**2)&-2)-1)*((n<<1)+m) # _Chai Wah Wu_, Aug 16 2022
%Y Cf. A075317, A075318, A075319.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Sep 14 2002
%E More terms from _R. J. Mathar_, Nov 12 2006
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