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
Examples
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 ... ...
Links
Programs
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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
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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 *)