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

1,3

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150, flattened)

Example

1
1 3
1 4 16
1 3 9 27
1 6 36 216 1296
1 5 25 125 625 3125
...

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

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 *)

Crossrefs

Cf. A110737, A110738, A110739.

Sequence in context: A066712 A064809 A058361 * A016734 A272473 A375299

Adjacent sequences: A112665 A112666 A112667 * A112669 A112670 A112671

Keyword

easy,nonn,tabl

Author

Amarnath Murthy, Aug 10 2005

Extensions

More terms from R. J. Mathar, Mar 13 2007

Status

approved