A280244 Lexicographically ordered list of sequences that meet the criteria for R. L. Graham's sequence: k = a_1 < a_2 < ... < a_t = A006255(k) and a_1*a_2*...*a_t is a square.

1, 2, 3, 4, 6, 2, 3, 6, 3, 4, 6, 8, 3, 6, 8, 4, 5, 8, 9, 10, 5, 8, 10, 6, 8, 9, 12, 6, 8, 12, 7, 8, 9, 14, 7, 8, 14, 8, 9, 10, 12, 15, 8, 10, 12, 15, 9, 10, 12, 15, 16, 18, 10, 12, 15, 18, 11, 12, 14, 16, 21, 22, 11, 12, 14, 21, 22, 11, 12, 15, 16, 18, 20, 22

Offset

1,2

Comments

A259527(n) rows begin with n.

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Example

[8,9,10,12,15] appears as a row in the table because A006255(8) = 15 and the product of the row is a square: 8*9*10*12*15 = 360^2.
Table begins:
  1;
  2,  3,  4,  6;
  2,  3,  6;
  3,  4,  6,  8;
  3,  6,  8;
  4;
  5,  8,  9, 10;
  5,  8, 10;
  6,  8,  9, 12;
  6,  8, 12;
  7,  8,  9, 14;
  7,  8, 14;
  8,  9, 10, 12, 15;
  8, 10, 12, 15;
  ...

Mathematica

MapIndexed[With[{b = #1, a = First@ #2}, Reverse@ Select[Rest@ Subsets@ Range[a, b], And[SubsetQ[#, {a, b}], IntegerQ@ Sqrt[Times @@ #]] &]] &, #] &@ Table[k = 0; Which[IntegerQ@ Sqrt@ n, k, And[PrimeQ@ n, n > 3], k = n, True, While[Length@ Select[n Map[Times @@ # &, n + Rest@ Subsets@ Range@ k], IntegerQ@ Sqrt@# &] == 0, k++]]; k + n, {n, 16}] // Flatten (* Michael De Vlieger, Dec 30 2016 *)

Crossrefs

Cf. A006255, A245499, A259527.

Sequence in context: A004567 A344340 A030378 * A203138 A249900 A260272

Adjacent sequences: A280241 A280242 A280243 * A280245 A280246 A280247

Keyword

nonn,tabf,look

Author

Peter Kagey, Dec 29 2016

Status

approved