A100348 Numbers n such that n-4^k is a prime for all k > 0 with 4^k < n.

6, 7, 9, 11, 15, 21, 23, 27, 33, 35, 45, 47, 57, 63, 75, 77, 83, 87, 105, 117, 143, 153, 167, 195, 215, 227, 243, 245, 255, 287, 297, 413, 437, 447, 483, 495, 507, 525, 573, 635, 657, 677, 755, 825, 1113, 1133, 1295, 1487, 1515, 1547, 1617, 1623, 2015, 2043, 2397

Offset: 1

Author

T. D. Noe, Nov 18 2004

Keywords

• nonn

Comments

The largest term appears to be 5833497. No others < 10^9; conjectured to be finite. Similar to A067528, which also contains 5 and 17, but a more direct generalization of A039669, a problem due to Erdos.

Examples

			27 is here because 27-4 and 27-16 are primes.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..100
• Walter E. Mientka and Roger C. Weitzenkamp, On f-plentiful numbers, Journal of Combinatorial Theory, Volume 7, Issue 4, December 1969, Pages 374-377

Crossrefs

Cf. A039669 (n such that n-2^k is prime), A067528 (n such that n-4^k is prime or 1).

Programs

Mathematica

lst={}; Do[k=1; While[p=n-4^k; p>0 && PrimeQ[p], k++ ]; If[p<=0, AppendTo[lst, n]], {n, 5, 10^7}]; lst