A168654 -id:A168654 - cp's OEIS frontend

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

Original entry on oeis.org

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

Amiram Eldar, May 28 2021

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).

			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.

Cf. A168512, A168654.

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

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

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