A109314 Numbers n such that prime(n) + n is a prime power (A246547).

3, 5, 8, 9, 12, 86, 230, 503, 1170, 2660, 2772, 6288, 6572, 8858, 9590, 14870, 16332, 17708, 53132, 54540, 63890, 64908, 82830, 93068, 98132, 104726, 119298, 136502, 152198, 177918, 187040, 234650, 241682, 253118, 263930, 278970, 376680, 412440, 456110, 469034

Offset: 1

Author

Zak Seidov and Robert G. Wilson v, Jun 25 2005

Keywords

• nonn

Examples

			2660 is OK because prime(2660) + 2660 = 23909 + 2660 = 26569 = 163^2, 163 is prime.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A025475 = powers of a prime but not prime, also nonprime n such that sigma(n)*phi(n) > (n-1)2; A107708 = values of q, A107709 = values of k; A107710 = values of prime (A109314(n)).

Cf. A107605, A246547.

Programs

Maple

ispp:= n -> not isprime(n) and nops(numtheory:-factorset(n))=1:
p:= 1: Res:= NULL:
for n from 1 to 10^6 do
  p:= nextprime(p);
  if ispp(n+p) then Res:= Res, n fi
od:
Res; # Robert Israel, Jun 08 2016

Mathematica

lst = {}; fQ[n_] := Block[{pf = FactorInteger[n]}, (2-Length[pf])(pf[[1, 2]]-1) > 0]; Do[ If[ fQ[Prime[n] + n], Print[n]; AppendTo[lst, n]], {n, 456109}]; lst

PARI

isok(n) = isprimepower(n+prime(n)) >= 2; \\ Michel Marcus, Jun 18 2017

Sage

def np(n): return n+nth_prime(n)
[n for n in (1..10000) if not np(n).is_prime() and np(n).is_prime_power()] # Giuseppe Coppoletta, Jun 08 2016

Formula

prime(n) + n = q^k, q is prime and k_Integer >= 2.