A381328 a(n+1) is the least k such that k - (a(n-1)+a(n)) and k + (a(n-1)+a(n)) are primes; a(0)=0, a(1)=1.

0, 1, 4, 8, 17, 28, 52, 83, 142, 232, 377, 614, 996, 1641, 2642, 4290, 6945, 11246, 18198, 29457, 47662, 77124, 124797, 201928, 326736, 528723, 855464, 1384230, 2239797, 3624050, 5863850, 9487911, 15351768, 24839684, 40191555, 65031270, 105222856, 170254137, 275477064, 445731218, 721208325, 1166939604

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..4759

Example

a(5) = 28 because a(3) + a(4) = 8 + 17 = 25, 28 - 25 = 3 and 28 + 25 = 53 are prime, and no smaller number works.

Maple

A[0]:= 0: A[1]:= 1:
for i from 2 to 50 do
  p:= 0;
  do
    p:= nextprime(p);
    if isprime(p + 2*(A[i-1]+A[i-2])) then
      A[i]:= p + A[i-1]+A[i-2];
      break
    fi
  od
od:
seq(A[j], j=0..50);

Mathematica

s={0, 1}; Do[k=s[[-1]]+s[[-2]]; Until[PrimeQ[k-s[[-1]]-s[[-2]]]&&PrimeQ[k+s[[-1]]+s[[-2]]], k++]; AppendTo[s, k], {n, 40}]; s (* James C. McMahon, Feb 21 2025 *)

Crossrefs

Sequence in context: A092321 A366157 A366069 * A026353 A067773 A301145

Adjacent sequences: A381325 A381326 A381327 * A381329 A381330 A381331

Keyword

nonn

Author

Robert Israel, Feb 20 2025

Status

approved