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

1,2

Links

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

Formula

a(2^n)=2^n.

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

Example

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; ...

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

Prog

(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)))

Crossrefs

Cf. A088370 (triangle).

Sequence in context: A121895 A139555 A241814 * A133181 A286280 A290088

Adjacent sequences: A088368 A088369 A088370 * A088372 A088373 A088374

Keyword

nonn

Author

Paul D. Hanna, Sep 28 2003

Status

approved