%I #10 Dec 31 2023 00:21:41

%S 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,

%T 26,29,27,28,38,54,40,52,42,50,44,48,46,66,51,41,53,39,55,37,57,35,31,

%U 61,33,59,58,34,60,72,45,47,65,67,88,70,62,30,36,56,76,79,104,80

%N 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.

%H Éric Angelini, <a href="https://cinquantesignes.blogspot.com/2023/12/palindromes-with-distinct-prime-factors.html">Sums of distinct prime factors</a>, Personal blog, December 2023.

%e a(1) + a(2) = 1 + 13 = 14 whose sopf is 9, a perfect square.

%e a(2) + a(3) = 13 + 15 = 28 whose sopf is 9, a perfect square.

%e a(7) + a(8) = 18 + 21 = 39 whose sopf is 16, a perfect square.

%e a(8) + a(9) = 21 + 7 = 28 whose sopf is 9, a perfect square.

%t 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]

%Y Cf. A008472, A164722.

%K nonn

%O 1,2

%A _Giorgos Kalogeropoulos_ and _Eric Angelini_, Dec 05 2023