proposed

approved

editing

proposed

Cf. also A341510, A341520, A351961, A351962.

<a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

Cf. A005940, A156552.

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

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

Cf. also A341520, A351961, A351962.

allocated for Antti KarttunenSquare 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

0,2

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.

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,

(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];

Cf. A297163 (row/column 0).

Cf. also A341520.

allocated

nonn,tabl

Antti Karttunen, Feb 26 2022

approved

editing

allocated for Antti Karttunen

allocated

approved