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

1,1

Links

Table of n, a(n) for n=1..55.

Formula

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

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

Prog

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

Crossrefs

Cf. A075317, A075318, A075320.

Sequence in context: A035401 A139330 A051448 * A030470 A326004 A297358

Adjacent sequences: A075316 A075317 A075318 * A075320 A075321 A075322

Keyword

nonn

Author

Amarnath Murthy, Sep 14 2002

Extensions

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

Status

approved