A228132 First differences of A014311.

4, 2, 1, 5, 2, 1, 3, 1, 2, 7, 2, 1, 3, 1, 2, 5, 1, 2, 4, 11, 2, 1, 3, 1, 2, 5, 1, 2, 4, 9, 1, 2, 4, 8, 19, 2, 1, 3, 1, 2, 5, 1, 2, 4, 9, 1, 2, 4, 8, 17, 1, 2, 4, 8, 16, 35, 2, 1, 3, 1, 2, 5, 1, 2, 4, 9, 1, 2, 4, 8, 17, 1, 2, 4, 8, 16, 33, 1, 2, 4, 8, 16, 32

Offset: 1

Author

Jon Perry, Nov 02 2013

Keywords

• nonn
• base

Comments

The records are: 4, 5, 7, 11, 19, 35, 67, ... and they occur at these indices of A014311: 11, 19, 35, 67, ... (for both, see A062709). - Michel Marcus, Jun 11 2015

The record (maximum) among the first 1000 terms is 65539. - Harvey P. Dale, May 29 2018

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A062709 (2^n+3), A014311 (numbers with exactly 3 ones in binary expansion).

Cf. A145057.

Programs

JavaScript

oo=0;
for (i=1;i<500;i++) {
s=i.toString(2);
o=0;
for (j=0;j
				

Mathematica

Differences[Select[Range[500],DigitCount[#,2,1]==3&]] (* Harvey P. Dale, May 29 2018 *)

PARI

lista(nn) = {my(last = 0); for (n=1, nn, if (hammingweight(n)==3, if (last, print1(n-last,", ")); last = n;););} \\ Michel Marcus, Jun 10 2015

Python

from math import isqrt, comb
from sympy import integer_nthroot
def A228132(n): return (1<<(r:=n-comb((m:=integer_nthroot(6*n+6,3)[0])+(t:=(n>=comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+(1<<(a:=isqrt(s:=n+1-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+(1<comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))-(1<<(a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))-(1<Chai Wah Wu, Apr 07 2025