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

1,13

Links

Table of n, a(n) for n=1..105.

Index entries for sequences computed from indices in prime factorization

Example

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,

Prog

(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];

Crossrefs

Cf. A252464 (main diagonal).

Cf. A005940, A156552, A348041.

Cf. also A347380, A347381.

Sequence in context: A117201 A060953 A339367 * A082858 A363164 A255318

Adjacent sequences: A348037 A348038 A348039 * A348041 A348042 A348043

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 27 2021

Status

approved