OFFSET
1,1
COMMENTS
Other such terms are 18806843674476 and 18806855958880.
a(n) is even. Proof: If a(n) = b is odd then c = a(n) + 1 where gcd(b, c) = 1 and d = c-b = 1 which is a square. Contradiction. - David A. Corneth, May 01 2022
EXAMPLE
If b = 6, then c = 25 and d = c-b = 19 (prime), so 6 is not in the sequence.
If b = 67613590, then c = 67613611, and d = c-b = 21 (neither prime nor square), so 67613590 is in the sequence.
MATHEMATICA
c[n_]:=Module[{k=n+1}, While[GCD[n, k]!=1||PrimeQ[k], k++]; k];
Select[Range[10^8], CompositeQ[#]&&CompositeQ[c[#]-#]&&!IntegerQ[Sqrt[c[#]-#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Fausto Morales Díaz and Ivan N. Ianakiev, Apr 30 2022
STATUS
approved