A067528 Numbers n such that n - 4^k is a prime or 1 for all k > 0 and n > 4^k.

5, 6, 7, 9, 11, 15, 17, 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

Offset: 1

Author

Amarnath Murthy, Feb 17 2002

Keywords

• nonn

Comments

Is the sequence finite?

The last term appears to be 5833497. - T. D. Noe, Nov 23 2004

A less strict version of A039669, n - 2^k is prime for 0 < k < log_2 k. If a number is in that sequence, then obviously it is also in this sequence. As of this writing, 105 is believed to be the last term of that sequence. - Alonso del Arte, May 24 2017

Examples

			167 is a term as 167 - 4 = 163, 167 - 16 = 151, 167 - 64 = 103 are primes.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..102 (no others < 2*10^9)

Crossrefs

Cf. A067526.

Programs

Maple

filter:= proc(n) local k, t;
  for k from 1 do
    if 4^k >= n-1 then return true
    elif not isprime(n-4^k) then return false
    fi
  od
end proc:
select(filter, [$5..3000]); # Robert Israel, May 24 2017

Mathematica

A067528 = {}; Do[k = 1; While[p = n - 4^k; p > 0 && (p == 1 || PrimeQ[p]), k++]; If[p <= 0, AppendTo[A067528, n]], {n, 5, 10^7}]; A067528 (* T. D. Noe *)

Extensions

More terms from Sascha Kurz, Mar 19 2002