A075319 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.

4, 14, 20, 30, 40, 46, 56, 62, 72, 82, 88, 98, 108, 114, 124, 130, 140, 150, 156, 166, 172, 182, 192, 198, 208, 218, 224, 234, 240, 250, 260, 266, 276, 286, 292, 302, 308, 318, 328, 334, 344, 350, 360, 370, 376, 386, 396, 402, 412, 418, 428, 438, 444, 454, 460

Offset: 1

Author

Amarnath Murthy, Sep 14 2002

Keywords

• nonn

Crossrefs

Cf. A075317, A075318, A075320.

Programs

Maple

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

Python

from math import isqrt
def A075319(n): return (n+isqrt(5*n**2)&-2)+n-1<<1 # Chai Wah Wu, Aug 16 2022

Formula

a(n) = A075317(n)+A075318(n). - R. J. Mathar, Nov 12 2006

Extensions

More terms from R. J. Mathar, Nov 12 2006