A128218 First differences of A128217.

1, 3, 1, 3, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

John W. Layman, Feb 19 2007

Keywords

• nonn

Comments

a(A130883(n-1)) = 2*n-1 and a(m) != 2*n-1 for m < A130883(n-1). - Reinhard Zumkeller, Jun 20 2015

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A128127.

Cf. A130883, A152271 (run lengths after initial term).

Programs

Haskell

a128218 n = a128218_list !! (n-1)
a128218_list = zipWith (-) (tail a128217_list) a128217_list
-- Reinhard Zumkeller, Jun 20 2015

Mathematica

nsrQ[n_]:=Module[{sr=Sqrt[n]},Abs[First[sr-Nearest[{Floor[sr], Ceiling[ sr]}, sr]]]<1/4];Differences[Select[Range[0,250],nsrQ]] (* Harvey P. Dale, May 02 2012 *)

PARI

default(realprecision, 10000);
is_A128217(n) = ((abs(sqrt(n)-sqrtint(n))<(1/4)) || (abs(sqrt(n)-(1+sqrtint(n)))<(1/4)));
k=0; n=0; prevm=0; while(k<20000, n++; if(is_A128217(n), k++; write("b128218.txt", k, " ", (n-prevm)); prevm = n)); \\ Antti Karttunen, Jan 16 2025

Formula

Let A(1)={1}. Then, for k=2,3,4,..., form A(k) by appending to A(k-1) the term k-1 followed by k-1 1's, if k is even, or by appending to A(k-1) the term k followed by k-1 1's, if k is odd. {a(n)} appears to be the limit of {A(k)} as k->infinity.

Extensions

Offset changed by Reinhard Zumkeller, Jun 20 2015