A348040 Square array A(n,k) = the length of the common prefix in binary expansions of A156552(n) and A156552(k), read by antidiagonals.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 1, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 1, 2, 1, 3, 1, 2, 1, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 0, 1, 1, 2, 3, 3, 3, 2, 1, 1, 0, 0, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 0, 0, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 3, 1, 1, 1, 1, 3, 1, 2, 1, 0

Offset: 1

Author

Antti Karttunen, Sep 27 2021

Keywords

• nonn
• tabl

Examples

			The top left 17x17 corner of the array:
  n/k | 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17
------+----------------------------------------------------
   1  | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   2  | 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
   3  | 0, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2,
   4  | 0, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1,
   5  | 0, 1, 2, 1, 3, 2, 3, 1, 1, 3, 3, 2, 3, 3, 2, 1, 3,
   6  | 0, 1, 2, 1, 2, 3, 2, 1, 1, 2, 2, 3, 2, 2, 3, 1, 2,
   7  | 0, 1, 2, 1, 3, 2, 4, 1, 1, 3, 4, 2, 4, 4, 2, 1, 4,
   8  | 0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 3, 1,
   9  | 0, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 1,
  10  | 0, 1, 2, 1, 3, 2, 3, 1, 1, 4, 3, 2, 3, 3, 2, 1, 3,
  11  | 0, 1, 2, 1, 3, 2, 4, 1, 1, 3, 5, 2, 5, 4, 2, 1, 5,
  12  | 0, 1, 2, 1, 2, 3, 2, 1, 1, 2, 2, 4, 2, 2, 3, 1, 2,
  13  | 0, 1, 2, 1, 3, 2, 4, 1, 1, 3, 5, 2, 6, 4, 2, 1, 6,
  14  | 0, 1, 2, 1, 3, 2, 4, 1, 1, 3, 4, 2, 4, 5, 2, 1, 4,
  15  | 0, 1, 2, 1, 2, 3, 2, 1, 1, 2, 2, 3, 2, 2, 4, 1, 2,
  16  | 0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1,
  17  | 0, 1, 2, 1, 3, 2, 4, 1, 1, 3, 5, 2, 6, 4, 2, 1, 7,
		

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A252464 (main diagonal).

Cf. A005940, A156552, A348041.

Cf. also A347380, A347381.

Programs

PARI

up_to = 105;
Abincompreflen(n, m) = { my(x=binary(n),y=binary(m),u=min(#x,#y)); for(i=1,u,if(x[i]!=y[i],return(i-1))); (u);};
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A348040sq(x,y) = Abincompreflen(A156552(x), A156552(y));
A348040list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A348040sq(col,(a-(col-1))))); (v); };
v348040 = A348040list(up_to);
A348040(n) = v348040[n];