A351960 Square array A(n,k) = A156552(A005940(1+n) + A005940(1+k)), read by antidiagonals.

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 9, 7, 7, 7, 7, 7, 9, 6, 16, 6, 6, 6, 6, 16, 6, 7, 9, 11, 9, 9, 9, 11, 9, 7, 16, 6, 16, 32, 16, 16, 32, 16, 6, 16, 15, 11, 9, 11, 17, 11, 17, 11, 9, 11, 15, 32, 64, 32, 16, 32, 10, 10, 32, 16, 32, 64, 32, 65, 17, 13, 17, 11, 17, 13, 17, 11, 17, 13, 17, 65

Offset

0,2

Comments

The indices run as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), etc. The array is symmetric.

Links

Table of n, a(n) for n=0..90.

Index entries for sequences related to binary expansion of n

Example

The top left corner of the array:
     |n= 0    1    2     3    4     5    6    7    8     9    10    11    12
-----+--------------------------------------------------------------------------
k= 0 |   1,   2,   3,    4,   5,    8,   9,   6,   7,   16,   15,   32,   65,
   1 |   2,   3,   4,    5,   8,    7,  16,   9,   6,   11,   64,   17,   14,
   2 |   3,   4,   5,    8,   7,    6,  11,  16,   9,   32,   13,   10,   35,
   3 |   4,   5,   8,    7,   6,    9,  32,  11,  16,   17,  128,   15,  512,
   4 |   5,   8,   7,    6,   9,   16,  17,  32,  11,   10,   19,   64,   21,
   5 |   8,   7,   6,    9,  16,   11,  10,  17,  32,   15,   18,   13, 1024,
   6 |   9,  16,  11,   32,  17,   10,  13,  64,  15,  128,   23,   18,  129,
   7 |   6,   9,  16,   11,  32,   17,  64,  15,  10,   13,  256,   19,   34,
   8 |   7,   6,   9,   16,  11,   32,  15,  10,  17,   64,   33,  128,   31,
   9 |  16,  11,  32,   17,  10,   15, 128,  13,  64,   19,   12,   33,   20,
  10 |  15,  64,  13,  128,  19,   18,  23, 256,  33,   12,   21,   14,   39,
  11 |  32,  17,  10,   15,  64,   13,  18,  19, 128,   33,   14,   23, 2048,
  12 |  65,  14,  35,  512,  21, 1024, 129,  34,  31,   20,   39, 2048,   25,
  13 | 128,  19,  18,   33, 256,   23,  14,  65,  12,   35,   34,   21, 8192,
  14 |  35, 512,  21, 1024,  31,   34,  27,  20, 129, 2048,   37,   66,  131,
  15 |  64,  13, 128,   19,  18,   33,  12,  23, 256,   65, 1024,   35, 4096,
  16 |  11,  32,  17,   10,  15,   64,  19, 128,  13,   18,   65,  256,   27,

Prog

(PARI)
up_to = 104;
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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 };
A351960sq(n, k) = A156552(A005940(1+n)+A005940(1+k));
A351960list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0, oo, for(col=0, a, i++; if(i > #v, return(v)); v[i] = A351960sq(col, (a-(col))))); (v); };
v351960 = A351960list(up_to);
A351960(n) = v351960[1+n];

Crossrefs

Cf. A005940, A156552.

Cf. A005408 (main diagonal), A297163 (row/column 0).

Cf. also A341510, A341520, A351961, A351962.

Sequence in context: A196238 A087843 A087831 * A372759 A194327 A058032

Adjacent sequences: A351957 A351958 A351959 * A351961 A351962 A351963

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 26 2022

Status

approved