A389946 Minimum positive value k such that prime(n) - k^2 is a prime number, or 0 if no such positive k exists.

0, 1, 0, 2, 2, 0, 2, 4, 2, 4, 0, 0, 2, 6, 2, 4, 4, 0, 6, 2, 6, 6, 2, 4, 6, 2, 6, 2, 6, 2, 0, 2, 6, 6, 6, 12, 12, 6, 2, 4, 4, 12, 8, 6, 2, 6, 12, 12, 2, 6, 2, 4, 12, 10, 4, 6, 6, 12, 6, 2, 12, 4, 6, 2, 6, 2, 18, 12, 4, 6, 2, 14, 6, 6, 0, 2, 4, 18, 2, 6, 6, 12, 8, 6, 0, 2, 4, 6, 2, 18, 2, 4, 18, 2, 6, 2

Offset

1,4

Links

Table of n, a(n) for n=1..96.

Example

a(5) = 2 because prime(5) = 11 and 11 - 4 = 7, and 4, thus 2^2, is the smallest number for which this is true.

Mathematica

a[n_] := Module[{p = Prime[n], k = 1}, While[k^2 < p && !PrimeQ[p - k^2], k++]; If[k^2 > p, 0, k]]; Array[a, 100] (* Amiram Eldar, Jan 06 2026 *)

Prog

(PARI) a(n) = my(p=prime(n)); for(k=1, sqrtint(p), if (isprime(p-k^2), return(k))); 0; \\ Michel Marcus, Jan 06 2026

Crossrefs

Cf. A386600.

Sequence in context: A159916 A159286 A355837 * A372470 A261277 A006462

Adjacent sequences: A389943 A389944 A389945 * A389947 A389948 A389949

Keyword

nonn

Author

Leo Hennig, Jan 05 2026

Status

approved