A344783 Numbers k such that 1 + Sum_{i=1..k} floor(k/i)*(2^i) is a prime number.

1, 3, 4, 7, 18, 25, 26, 30, 40, 50, 95, 150, 348, 694, 1052, 1222, 1808, 2567, 4917, 5399, 7438, 10720, 12152, 30412, 38313, 53620, 121419, 123523

Offset: 1

Author

Amiram Eldar, May 28 2021

Keywords

• nonn
• more

Comments

Equivalently, numbers k such that A168512(2^k) is a prime number.

The corresponding primes are 3, 19, 41, 283, 525529, 67117859, 134234921, 2147551801, ...

If k is a term of this sequence then 2^k * A168512(2^k) is a term of A168654 (see Ray Chandler's comment in A168654).

Examples

			1 is a term since 1 + Sum_{i=1..1} floor(k/i)*(2^i) = 1 + 2 = 3 is a prime.
3 is a term since 1 + Sum_{i=1..3} floor(k/i)*(2^i) = 1 + 6 + 4 + 8 = 19 is a prime.
		

Crossrefs

Cf. A168512, A168654.

Programs

Mathematica

Select[Range[100], PrimeQ[1 + Sum[Floor[#/i]*2^i,{i, 1, #}]] &]

Extensions

a(27)-a(28) from Michael S. Branicky, Sep 23 2024