A359483 For n > 2, a(n) is the least prime p > a(n-1) such that a(n-1) + p is divisible by a(n-2); a(1) = 2, a(2) = 3.

2, 3, 5, 7, 13, 29, 101, 131, 677, 2467, 5657, 19013, 48871, 521519, 553643, 3618509, 14098067, 116168257, 193989217, 1200029867, 8887409417, 12713128189, 573855893333, 773735694701, 9555670385293, 30678585739159, 160434821966701, 1312137293512931, 2217428789754491, 100129280104254127

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..733

Example

a(3) = 5 because 5 is prime and a(2) + 5 = 8 is divisible by a(1) = 2.
a(4) = 7 because 7 is prime and a(3) + 7 = 12 is divisible by a(2) = 3.
a(5) = 13 because 13 is prime and a(4) + 13 = 20 is divisible by a(3) = 5.

Maple

p:= 2: q:= 3: R:= p, q: t:= 3: count:= 2:
while count < 40 do
  t:= t + p;
  if isprime(t) then
    R:= R, t; count:= count+1;
    p:= q; q:= t;
    t:= floor(2*q/p)*p-q;
  fi
od:
R;

Mathematica

nmax=17; a[1]=2; a[2]=3; For[n=3, n<=nmax,  n++, For[k=1, k>0, k++, If[Prime[k]>a[n-1] && Mod[a[n-1]+Prime[k], a[n-2]]==0, a[n]=Prime[k]; k=-1]]]; Array[a, nmax] (* Stefano Spezia, Apr 01 2023 *)

Crossrefs

Sequence in context: A167134 A071905 A306317 * A067573 A103199 A054217

Adjacent sequences: A359480 A359481 A359482 * A359484 A359485 A359486

Keyword

nonn

Author

Zak Seidov and Robert Israel, Mar 31 2023

Status

approved