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%I #32 Sep 08 2022 08:45:25
%S 1,2,3,5,7,9,11,17,23,25,27,29,41,47,59,71,79,81,101,107,125,137,149,
%T 167,179,191,197,227,239,241,269,281,311,347,359,419,431,461,521,569,
%U 599,617,641,659,727,809,821,827,839,857,881,1019,1031,1049,1061,1091
%N Numbers k such that k and k+2 are prime powers.
%C Twin prime powers, a generalization of the twin primes. The twin primes are a subsequence.
%C From _Daniel Forgues_, Aug 17 2009: (Start)
%C Numbers k such that k + (0, 2) is a prime power pair.
%C k + (0, 2m), m >= 1, being an admissible pattern for prime pairs has high density.
%C k + (0, 2m-1), m >= 1, being a non-admissible pattern for prime pairs, has low density [the only possible pairs are (2^a - 2m-1, 2^a) or (2^a, 2^a + 2m-1), a >= 0.] (End)
%H Amiram Eldar, <a href="/A120431/b120431.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1270 from Daniel Forgues)
%F a(n) = A064076(n-2) for n >= 3. - _Georg Fischer_, Nov 02 2018
%e a(5) = 7 since the 5th pair of twin prime powers is (7,9), while the first four pairs are (1,3), (2,4), (3,5) and (5,7).
%p isppow := proc(n) local pf; pf := ifactors(n)[2]; if nops(pf) = 1 or n =1 then true; else false; fi; end; isA120431 := proc(n) RETURN (isppow(n) and isppow(n+2)); end; for n from 1 to 1500 do if isA120431(n) then printf("%d, ",n); fi; od; # _R. J. Mathar_, Dec 16 2006
%t Join[{1}, Select[Range[1100], And@@PrimePowerQ/@{#, # + 2} &]] (* _Vincenzo Librandi_, Nov 03 2018 *)
%o (PARI) is(n)=if(n<4,return(n>0)); isprimepower(n) && isprimepower(n+2) \\ _Charles R Greathouse IV_, Apr 24 2015
%o (Magma) [1] cat [n: n in [2..1200] | IsPrimePower(n) and IsPrimePower(n+2)]; // _Vincenzo Librandi_, Nov 03 2018
%Y Cf. A001359, A000961, A064076.
%Y Cf. A006549, A164571, A164572, A164573, A164574.
%K nonn
%O 1,2
%A _Greg Huber_, Jul 13 2006
%E More terms from _R. J. Mathar_, Dec 16 2006
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