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 A267945 Primes that are a prime power plus two. 2
 5, 7, 11, 13, 19, 29, 31, 43, 61, 73, 83, 103, 109, 127, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The term 'prime power' refers to the elements of A246655. If we were to extend the definition of prime power to include 1, then 3 would be the first term of the sequence, because 3 = 2^0 + 2. The sequence is probably infinite, since it includes all the terms of A006512 (Greater of twin primes). From Robert Israel, Jan 22 2016: (Start) Since 3 divides p or p^k+2 if k is even, the only terms of the form p^k+2 where k is even are A228034. All terms not in A057735 are congruent to 1 mod 3. The generalized Bunyakovsky conjecture implies that for any odd k, there are infinitely many terms of the form p^k+2. (End) LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Wikipedia, Generalized Bunyakovsky conjecture EXAMPLE 5 is in the sequence because 5 = 3^1 + 2. 7 is in the sequence because 7 = 5^1 + 2. 11 is in the sequence because 11 = 3^2 + 2. 13 is in the sequence because 13 = 11^1 + 2. 29 is in the sequence because 29 = 3^3 + 2. MAPLE select(t -> isprime(t) and nops(numtheory:-factorset(t-2))=1, [ seq(i, i=3..1000, 2)]); # Robert Israel, Jan 22 2016 MATHEMATICA A267945Q = PrimeQ@# && (Length@# == 1 && #[[1, 1]] > 1 &@FactorInteger[# - 2]) & (* JungHwan Min, Jan 25 2016 *) Select[Array[Prime, 100], Length@# == 1 && #[[1, 1]] > 1 &@FactorInteger[# - 2] &] (* JungHwan Min, Jan 25 2016 *) PROG (Sage) filter( is_prime, [ n+2 for n in prime_powers( 1, 1000 ) ] ) (PARI) lista(nn) = {forprime(p=2, nn, if (isprimepower(p-2), print1(p, ", ")); ); } \\ Michel Marcus, Jan 22 2016 CROSSREFS Cf. A000961, A057735, A228034, A246655, A267944. Sequence in context: A081759 A155053 A152468 * A088664 A023219 A343448 Adjacent sequences: A267942 A267943 A267944 * A267946 A267947 A267948 KEYWORD nonn AUTHOR Robert C. Lyons, Jan 22 2016 STATUS approved

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Last modified September 10 00:26 EDT 2024. Contains 375769 sequences. (Running on oeis4.)