A367949 Lexicographically earliest sequence of distinct positive integers such that the sum of the distinct prime factors (sopf) of a(n) + a(n + 1) is a perfect square.

1, 13, 15, 24, 4, 10, 18, 21, 7, 32, 14, 25, 3, 11, 17, 22, 6, 8, 20, 19, 9, 5, 23, 16, 12, 2, 26, 29, 27, 28, 38, 54, 40, 52, 42, 50, 44, 48, 46, 66, 51, 41, 53, 39, 55, 37, 57, 35, 31, 61, 33, 59, 58, 34, 60, 72, 45, 47, 65, 67, 88, 70, 62, 30, 36, 56, 76, 79, 104, 80

Offset

1,2

Links

Table of n, a(n) for n=1..70.

Éric Angelini, Sums of distinct prime factors, Personal blog, December 2023.

Example

a(1) + a(2) =  1 + 13 = 14 whose sopf is  9, a perfect square.
a(2) + a(3) = 13 + 15 = 28 whose sopf is  9, a perfect square.
a(7) + a(8) = 18 + 21 = 39 whose sopf is 16, a perfect square.
a(8) + a(9) = 21 +  7 = 28 whose sopf is  9, a perfect square.

Mathematica

a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[ar=Array[a, n-1], k] ||!IntegerQ@Sqrt@Total[First/@FactorInteger[k+a[n-1]]], k++]; k); Array[a, 70]

Crossrefs

Cf. A008472, A164722.

Sequence in context: A067912 A140646 A109656 * A178724 A087814 A227449

Adjacent sequences: A367946 A367947 A367948 * A367950 A367951 A367952

Keyword

nonn

Author

Giorgos Kalogeropoulos and Eric Angelini, Dec 05 2023

Status

approved