A381368 a(n) is the least k > n for which prime(n) + prime(k) is a square.

4, 6, 5, 10, 16, 9, 8, 102, 13, 20, 30, 28, 17, 26, 16, 58, 33, 23, 55, 21, 54, 142, 30, 28, 49, 48, 139, 35, 91, 47, 45, 44, 56, 135, 54, 40, 39, 252, 51, 49, 78, 128, 62, 76, 75, 126, 245, 71, 55, 69, 54, 68, 120, 137, 81, 65, 63, 238, 171, 96, 62, 76, 108, 209

Offset: 1

Author

Felix Huber, Mar 02 2025

Keywords

• nonn
• easy

Comments

Least k > n for which A000040(n) + A000040(k) is a term of A000290.

a(1) = 1 if k = n were also permitted. All other terms would remain unchanged.

Examples

			a(2) = 6 because prime(2) + prime(6) = 3 + 13 = 4^2 and 3 + 5, 3 + 7, 3 + 11 are not squares.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000290, A259232.

Programs

Maple

A381368:=proc(n)
    local k;
        for k from n+1 do
            if issqr(ithprime(n)+ithprime(k)) then
                return k
            fi
        od
end proc;
seq(A381368(n),n=1..64);

Mathematica

a[n_]:=Module[{k=n+1},While[!IntegerQ[Sqrt[Prime[n]+Prime[k]]], k++]; k]; Array[a,64] (* Stefano Spezia, Mar 02 2025 *)

PARI

a(n) = my(k=n+1, q=prime(n+1), p=prime(n)); while (!issquare(p+q), k++;q=nextprime(q+1)); k; \\ Michel Marcus, Mar 02 2025

Formula

a(n) = A000720(A259232(n)). - Michel Marcus, Mar 02 2025