A101462 Smallest k such that 2^k-prime(n) is prime.

2, 3, 3, 39, 4, 4, 6, 5, 6, 5, 7, 11, 6, 29, 6, 6, 6, 6, 7, 10, 9, 9, 8, 8, 7, 26, 9, 8, 7, 10, 47, 14, 10, 9, 12, 31, 15, 9, 8, 8, 12, 9, 14, 21, 10, 9, 25, 261, 8, 9, 8, 8, 9, 8, 14, 10, 16, 9, 15, 10, 9, 12, 11, 14, 9, 12, 9, 791, 10, 9, 16, 20, 15, 9, 11, 10, 16, 15, 26, 9, 12, 11, 10

Offset: 1

Author

Lei Zhou, Jan 20 2005

Keywords

• nonn

Comments

Conjecture: sequence is defined for all n. First unproved n: 286 Prime(286)=1871, up to date, tested up to k=40959, none 2^k-Prime(286) is prime.

Primo was used for testing large primes.

Examples

			Prime(1)=2, 2^2-2 = 2 is prime
Prime(2)=3, 2^3-3 = 5 is prime
...
Prime(68)=337, 2^791-337 is prime.
		

Links

• Lei Zhou, Between 2^n and primes.

Crossrefs

Cf. A094076.

Programs

Mathematica

 f[n_] := Block[{p = Prime@ n}, k = Ceiling@ Log2@ p; While[! PrimeQ[2^k - p], k++]; k]; Array[f, 83]