A264734 Prime powers k such that k - 2 and k + 2 are prime powers.

3, 5, 7, 9, 11, 25, 27, 29, 81, 241, 59051, 450283905890997361, 36472996377170786401

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 22 2015

Keywords

• nonn
• more

Comments

From Robert Israel, Nov 22 2015: (Start)

a(14) > 3^1000 - 2 if it exists.

One of a(n), a(n)+2 and a(n)-2 must be a power of 3. (End)

Examples

			81 is in this sequence because 81 - 2 = 79, 81 and 81 + 2 = 83 are all prime powers.
		

Crossrefs

Cf. A000961, A144234, A264744.

Programs

Magma

[n: n in [5..100000] | IsPrimePower(n-2) and IsPrimePower(n) and IsPrimePower(n+2)];

Maple

ispp:= proc(x) local p, r;
  if isprime(x) then return true fi;
  p:= 2;
  do
     r:= iroot(x,p);
     if r^p = x then return isprime(r) fi;
     if r < 2 then return false fi;
     p:= nextprime(p);
  od:
end proc:
ispp(1):= true:
A:= NULL;
for n from 1 to 1000 do
  B:= map(ispp, [3^n-4,3^n-2,3^n+2,3^n+4]);
  if B[1] and B[2] then A:= A, 3^n-2 fi;
  if B[2] and B[3] then A:= A, 3^n fi;
  if B[3] and B[4] then A:= A, 3^n+2 fi;
od:
A; # Robert Israel, Nov 22 2015

Mathematica

Prepend[Select[Range@ 100000, AllTrue[{# - 2, #, # + 2}, PrimePowerQ] &], 3] (* Michael De Vlieger, Dec 03 2015, Version 10 *)

PARI

is(k) = isprimepower(k) || k==1;
for(k=1, 1e6, if(is(k) && is(k+2) && is(k-2), print1(k, ", "))) \\ Altug Alkan, Nov 22 2015

Extensions

a(12) and a(13) from Robert Israel, Nov 22 2015