A088371 Position where n is inserted into the n-th row of triangle A088370, where the n-th row differs from the prior row only by the presence of n.

1, 2, 2, 4, 2, 5, 4, 8, 2, 7, 5, 11, 4, 11, 8, 16, 2, 11, 7, 17, 5, 16, 11, 23, 4, 17, 11, 25, 8, 23, 16, 32, 2, 19, 11, 29, 7, 26, 17, 37, 5, 26, 16, 38, 11, 34, 23, 47, 4, 29, 17, 43, 11, 38, 25, 53, 8, 37, 23, 53, 16, 47, 32, 64, 2, 35, 19, 53, 11, 46, 29, 65, 7, 44, 26, 64, 17

Offset: 1

Author

Paul D. Hanna, Sep 28 2003

Keywords

• nonn

Examples

			A088370 rows: {1}, {1, 2}, {1, 3, 2}, {1, 3, 2, 4}, {1, 5, 3, 2, 4}, {1, 5, 3, 2, 6, 4}, {1, 5, 3, 7, 2, 6, 4}, ...
Row 5 is formed from row 3, {1, 3, 2} and row 2, {1, 2}: {1, 5, 3, 2, 4} = {1*2-1, 3*2-1, 2*2-1}|{1*2, 2*2}.
This sequence can form the following irregular triangle:
1;
2;
2, 4;
2, 5, 4, 8;
2, 7, 5, 11, 4, 11, 8, 16;
2, 11, 7, 17, 5, 16, 11, 23, 4, 17, 11, 25, 8, 23, 16, 32;
2, 19, 11, 29, 7, 26, 17, 37, 5, 26, 16, 38, 11, 34, 23, 47, 4, 29, 17, 43, 11, 38, 25, 53, 8, 37, 23, 53, 16, 47, 32, 64;
2, 35, 19, 53, 11, 46, 29, 65, 7, 44, 26, 64, 17, 56, 37, 77, 5, 46, 26, 68, 16, 59, 38, 82, 11, 56, 34, 80, 23, 70, 47, 95, 4, 53, 29, 79, 17, 68, 43, 95, 11, 64, 38, 92, 25, 80, 53, 109, 8, 65, 37, 95, 23, 82, 53, 113, 16, 77, 47, 109, 32, 95, 64, 128; ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..16384 (first 1024 terms from Paul D. Hanna)

Crossrefs

Cf. A088370 (triangle).

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
     `if`(n::odd, a(n/2+1/2), a(n/2)+n/2))
    end:
seq(a(n), n=1..128);  # Alois P. Heinz, Jul 26 2019

PARI

L=100; b=vector(L,k,k); c=vector(L); a=vector(L,k,b); a[1]=[1]; print1(1,","); for(n=2,L,i=floor((n+1)/2); j=floor(n/2); b=a[i]; b=vector(i,k,b[k]=2*b[k]-1 ); c=a[j]; c=vector(j,k,c[k]=2*c[k]); a[n]=concat(b,c); t=a[n]; for(k=1,n,if(t[k]==n,print1(k,","); k=n+1)))

Formula

a(2^n)=2^n.

a(2*n-1)=a(n), a(2*n)=n+a(n).