A355974 a(1) = 2. For n > 1, a(n) = 2*a(n-1) + p for the least prime p > 2*a(n-1) such that 2*a(n-1) + p is prime.

2, 11, 53, 233, 953, 3917, 15761, 63149, 252731, 1011221, 4045091, 16180391, 64721819, 258887357, 1035549707, 4142198861, 16568795489, 66275182097, 265100728391, 1060402913621, 4241611654871, 16966446620411, 67865786481743, 271463145927587, 1085852583711851, 4343410334847929, 17373641339392589

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..300

Example

a(3) = 53 because 31 is the least prime p > 2*a(2) = 22 such that 2*11 + p is prime, and 2*11 + 31 = 53.

Maple

f:= proc(b) local c;
    c:= 2*b;
    do
      c:= nextprime(c);
      if isprime(2*b+c) then return 2*b+c fi
    od
end proc:
R:= 2: p:= 2:
for i from 1 to 30 do
  p:= f(p);
  R:= R, p
od:
R;

Mathematica

a[1] = 2; a[n_] := a[n] = Module[{k = 2*a[n - 1], p}, p = NextPrime[k]; While[! PrimeQ[k + p], p = NextPrime[p]]; k + p]; Array[a, 25] (* Amiram Eldar, Jul 22 2022 *)

Crossrefs

Sequence in context: A052171 A333542 A168022 * A030281 A289847 A063767

Adjacent sequences: A355971 A355972 A355973 * A355975 A355976 A355977

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 21 2022

Status

approved