A169894 Table of carryless sums i + j, i>=0, j>=0, read by antidiagonals.

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 11, 11, 12, 12, 12, 2, 2, 2, 2, 2, 2, 2, 12, 12, 12

Offset

0,4

Links

Stefano Spezia, First 151 antidiagonals of the table, flattened

Index entries for sequences related to carryless arithmetic

Example

Table begins:
  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ...
  1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 12, 13, 14, 15, 16 ...
  2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 12, 13, 14, 15, 16, 17 ...
  3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 13, 14, 15, 16, 17, 18 ...
  4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 14, 15, 16, 17, 18, 19 ...
  ...

Maple

A169894 := proc(a, b)
    local adigs, bdigs, cdigs ;
    adigs := convert(a, base, 10) ;
    bdigs := convert(b, base, 10) ;
    len := max(nops(adigs), nops(bdigs)) ;
    adigs := [op(adigs), seq(0, d=1..len-nops(adigs))] ;
    bdigs := [op(bdigs), seq(0, d=1..len-nops(bdigs))] ;
    cdigs := [] ;
    for d from 1 to len do
        cdigs := [op(cdigs), A010879(op(d, adigs)+op(d, bdigs))] ;
    end do:
    add(op(d, cdigs)*10^(d-1), d=1..len) ;
end proc: # R. J. Mathar, Jul 12 2013

Mathematica

len[num_]:=Length[IntegerDigits[num]]; digit[num_, d_]:=Part[IntegerDigits[num], d]; T[i_, j_] := FromDigits[Reverse[CoefficientList[PolynomialMod[Sum[digit[i, c]*x^(len[i]-c), {c, len[i]}]+Sum[digit[j, r]*x^(len[j]-r), {r, len[j]}], 10], x]]]; Table[T[i - j, j], {i, 0, 12}, {j, 0, i}] (* Stefano Spezia, Dec 20 2023 *)

Crossrefs

Cf. A004520 (diagonal), A059692 (carryless products).

Sequence in context: A214972 A225687 A083291 * A357930 A003056 A117707

Adjacent sequences: A169891 A169892 A169893 * A169895 A169896 A169897

Keyword

nonn,base,look,tabl

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 06 2010

Status

approved