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

1,2

Links

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

Formula

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

Example

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 ...
  ...

Prog

(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

Crossrefs

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

Sequence in context: A123966 A371898 A079507 * A116866 A126280 A170986

Adjacent sequences: A098361 A098362 A098363 * A098365 A098366 A098367

Keyword

nonn,tabl,base

Author

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

Extensions

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

Status

approved