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%I #13 Aug 17 2022 03:11:02
%S 4,14,20,30,40,46,56,62,72,82,88,98,108,114,124,130,140,150,156,166,
%T 172,182,192,198,208,218,224,234,240,250,260,266,276,286,292,302,308,
%U 318,328,334,344,350,360,370,376,386,396,402,412,418,428,438,444,454,460
%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 sum of the members of pairs.
%F a(n) = A075317(n)+A075318(n). - _R. J. Mathar_, Nov 12 2006
%p A075319 := proc(nmax) local r,k,a,pairs ; a := [4] ; 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),2*(r+k)] ; pairs := [op(pairs),r,r+2*k] ; k := k+1 ; od ; RETURN(a) ; end: a := A075319(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 A075319(n): return (n+isqrt(5*n**2)&-2)+n-1<<1 # _Chai Wah Wu_, Aug 16 2022
%Y Cf. A075317, A075318, A075320.
%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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