A112668 Triangle read by rows: row n gives an n-term geometric progression with first term 1 such that the sum of the n terms is a multiple of n.
1, 1, 3, 1, 4, 16, 1, 3, 9, 27, 1, 6, 36, 216, 1296, 1, 5, 25, 125, 625, 3125, 1, 8, 64, 512, 4096, 32768, 262144, 1, 3, 9, 27, 81, 243, 729, 2187, 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 1, 9, 81, 729, 6561, 59049, 531441, 4782969, 43046721, 387420489, 1
Offset: 1
Examples
1 1 3 1 4 16 1 3 9 27 1 6 36 216 1296 1 5 25 125 625 3125 ...
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150, flattened)
Programs
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Maple
A112668 := proc(n) local a2,i,a ; a2 := 2 ; while (1-a2^n)/(1-a2) mod n <> 0 do a2 := a2+1 ; od ; a := [] ; for i from 1 to n do a := [op(a), a2^(i-1)] ; od ; RETURN(a) ; end: for row from 1 to 14 do r := A112668(row) : for n from 1 to nops(r) do printf("%d, ",op(n,r)) ; od : od : # R. J. Mathar, Mar 13 2007
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Mathematica
Block[{a = {{1}}, k, s}, Do[k = 2; While[Mod[Total@ Set[s, NestList[# k &, 1, i - 1]], i] != 0, k++]; AppendTo[a, s], {i, 2, 10}]; a] // Flatten (* Michael De Vlieger, Dec 31 2020 *)
Extensions
More terms from R. J. Mathar, Mar 13 2007