A098364 Multiplication table of the digits of the square root of 2 read by antidiagonals.

1, 4, 4, 1, 16, 1, 4, 4, 4, 4, 2, 16, 1, 16, 2, 1, 8, 4, 4, 8, 1, 3, 4, 2, 16, 2, 4, 3, 5, 12, 1, 8, 8, 1, 12, 5, 6, 20, 3, 4, 4, 4, 3, 20, 6, 2, 24, 5, 12, 2, 2, 12, 5, 24, 2, 3, 8, 6, 20, 6, 1, 6, 20, 6, 8, 3, 7, 12, 2, 24, 10, 3, 3, 10, 24, 2, 12, 7, 3, 28, 3, 8, 12, 5, 9, 5, 12, 8, 3, 28, 3

Offset: 1

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004

Keywords

• nonn
• tabl
• base

Examples

			Triangle begins:
  1;
  4,4;
  1,16,1;
  4,4,4,4;
  ...
Array begins:
  1  4 1  4 2 ...
  4 16 4 16 8 ...
  1  4 1  4 2 ...
  4 16 4 16 8 ...
  2  8 2  8 4 ...
  ...
		

Links

• Michel Marcus, Antidiagonals n = 1..100, flattened

Crossrefs

Cf. A002193, A003991, A098365, A098366, A098367.

Programs

PARI

sqrt2(nn) = {my(r=0, x=2, list = List(), d); for(digits=1, nn, d=0; while((20*r+d)*d <= x, d++); d--; listput(list, d); x=100*(x-(20*r+d)*d); r=10*r+d;); Vec(list);} \\ A002193
lista(nn) = {my(dd = sqrt2(nn)); for (n=1, nn, for (k=1, n, print1(dd[k]*dd[n-k+1], ", ")));} \\ Michel Marcus, Nov 11 2021

Formula

T(n,k) = A003991(A002193(n), A002193(k)). - Michel Marcus, Nov 03 2021

Extensions

Offset changed to 1 and a(34)=1 inserted by Georg Fischer, Nov 02 2021