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

Author

Ahmad J. Masad, Mar 09 2024

Keywords

• nonn

Examples

			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)
		

Links

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

Crossrefs

Cf. A108184, A056206.

Programs

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 *)