A343738 - OEIS

%I #7 Jul 02 2021 07:44:33

%S 3,5,11,549755813881,23,53,19,17,47,109,43,41,103,37,227,97,223,16349,

%T 2011,89,983,536870869,83,977,79,461,971,73,71,197,67,193,191,524221,

%U 443,953,439,181,179,433,431,173,130987,937,167,421,163,929,1951,157

%N a(n) is the smallest prime p > k such that p + k is a power of 2, where k = 2*n - 1, or 0 if no such prime exists.

%C k = 2*n-1 is the n-th odd number; p is the smallest prime > k such that p+k is a power of 2. If the constraint "> k" were removed, sequence A096822 would result.

%e For n=1, k = 2*n-1 = 1, and the smallest prime p > 1 such that p+1 is a power of 2 is 3, so a(1)=3.

%e For n=3, k=5, and the smallest prime p > 5 such that p+5 is a power of 2 is 11, so a(3)=11.

%e For n=4, k=7, and there is no prime in the sequence {2^4 - 7 = 9, 2^5 - 7 = 25, 2^6 - 7 = 57, ...} until 2^39 - 7 = 549755813881, so a(4) = 549755813881.

%e For n=55, k=109, and the smallest prime p > 109 such that p+109 is a prime is a(55) = 2^963 - 109 (a 290-digit number).

%Y Cf. A096822.

%K nonn

%O 1,1

%A _Jon E. Schoenfield_, Jun 27 2021