A358804 a(n) is the least nonnegative integer k such that (k^2 + prime(n)^2)/2 is prime but (k^2 + prime(i)^2)/2 is not prime for i < n.

0, 1, 3, 15, 31, 45, 143, 81, 233, 151, 71, 353, 141, 537, 457, 1663, 209, 391, 707, 1081, 1877, 1161, 3807, 2361, 5657, 1399, 2783, 2967, 3149, 2923, 5103, 1109, 11937, 7211, 2341, 9311, 6837, 10303, 24933, 8273, 11821, 9931, 11191, 6377, 14007, 48111, 12821, 43967, 27563, 17171, 38157, 16859

Offset

1,3

Links

Table of n, a(n) for n=1..52.

Formula

A358790((a(n)-1)/2) = prime(n) for n > 1.

Example

a(4) = 15 because prime(4) = 7 and (15^2 + 7^2)/2 = 137 is prime while (15^2 + p^2)/2 is not prime for primes p < 7, and 15 is the least number that works.

Maple

g:= proc(n) local s, p;
  s:= n^2; p:= 2;
  do
    p:= nextprime(p);
    if isprime((s+p^2)/2) then return p fi
  od
end proc:
N:= 100: # for a(1)..a(N)
M:= ithprime(N): V:= Vector(M, -1):
count:= 1: V[2]:= 0:
for n from 1 by 2 while count < N do
  v:= g(n); if v <= M and V[v] = -1 then V[v]:= n; count:= count+1 fi;
od:
seq(V[ithprime(i)], i=1..N);

Mathematica

a[n_] := Module[{p = Prime[n], k = 0}, While[! PrimeQ[(k^2 + p^2)/2] || AnyTrue[Prime[Range[n - 1]], PrimeQ[(k^2 + #^2)/2] &], k++]; k]; Array[a, 50] (* Amiram Eldar, Dec 01 2022 *)

Crossrefs

Cf. A358790.

Sequence in context: A289970 A211002 A031039 * A152813 A184235 A086381

Adjacent sequences: A358801 A358802 A358803 * A358805 A358806 A358807

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 01 2022

Status

approved