A371065 a(1)=2; for n > 1, a(n) is the least prime number p > a(n-1) such that p + 2^(n-1) is a prime number.

2, 3, 7, 11, 13, 29, 37, 53, 61, 89, 127, 131, 157, 197, 223, 269, 307, 359, 367, 419, 463, 491, 547, 593, 607, 641, 643, 701, 823, 947, 1213, 1229, 1237, 1319, 1327, 1451, 1723, 2381, 3019, 3299, 3307, 3371, 3847, 4493, 4621, 4931, 5179, 5783, 6043, 6197, 6469

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..5000

Example

For n=5, the preceding term a(4)=11 and 2^(5-1)=16, so a(5) is the least prime p > 11 such that p+16 is a prime too, which is p = 13 = a(5).
From Michael De Vlieger, Mar 10 2024: (Start)
Table of first terms:
   n   a(n)  2^(n+1)  a(n)+2^(n+1)
  -------------------------------
   1      2       1         3
   2      3       2         5
   3      7       4        11
   4     11       8        19
   5     13      16        29
   6     29      32        61
   7     37      64       101
   8     53     128       181
   9     61     256       317
  10     89     512       601
  11    127    1024      1151
  12    131    2048      2179
  ... (End)

Mathematica

a[1] = 2; a[n_] := a[n] = Module[{p = NextPrime[a[n - 1]]}, While[! PrimeQ[p + 2^(n - 1)], p = NextPrime[p]]; p]; Array[a, 50] (* Amiram Eldar, Mar 10 2024 *)

Crossrefs

Cf. A108184, A056206.

Sequence in context: A145032 A233414 A233863 * A233194 A233040 A233769

Adjacent sequences: A371062 A371063 A371064 * A371066 A371067 A371068

Keyword

nonn

Author

Ahmad J. Masad, Mar 09 2024

Status

approved