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A120431 Numbers k such that k and k+2 are prime powers. 7
1, 2, 3, 5, 7, 9, 11, 17, 23, 25, 27, 29, 41, 47, 59, 71, 79, 81, 101, 107, 125, 137, 149, 167, 179, 191, 197, 227, 239, 241, 269, 281, 311, 347, 359, 419, 431, 461, 521, 569, 599, 617, 641, 659, 727, 809, 821, 827, 839, 857, 881, 1019, 1031, 1049, 1061, 1091 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Twin prime powers, a generalization of the twin primes. The twin primes are a subsequence.

From Daniel Forgues, Aug 17 2009: (Start)

Numbers k such that k + (0, 2) is a prime power pair.

k + (0, 2m), m >= 1, being an admissible pattern for prime pairs has high density.

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)

LINKS

Daniel Forgues, Table of n, a(n) for n = 1..1270

FORMULA

a(n) = A064076(n-2) for n >= 3. - Georg Fischer, Nov 02 2018

EXAMPLE

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).

MAPLE

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

MATHEMATICA

Join[{1}, Select[Range[1100], And@@PrimePowerQ/@{#, # + 2} &]] (* Vincenzo Librandi, Nov 03 2018 *)

PROG

(PARI) is(n)=if(n<4, return(n>0)); isprimepower(n) && isprimepower(n+2) \\ Charles R Greathouse IV, Apr 24 2015

(MAGMA) [1] cat [n: n in [2..1200] | IsPrimePower(n) and IsPrimePower(n+2)]; // Vincenzo Librandi, Nov 03 2018

CROSSREFS

Cf. A001359, A000961, A064076.

Cf. A006549, A164571, A164572, A164573, A164574.

Sequence in context: A281541 A066824 A036963 * A214548 A254440 A284914

Adjacent sequences:  A120428 A120429 A120430 * A120432 A120433 A120434

KEYWORD

nonn

AUTHOR

Greg Huber, Jul 13 2006

EXTENSIONS

More terms from R. J. Mathar, Dec 16 2006

STATUS

approved

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Last modified March 22 12:39 EDT 2019. Contains 321421 sequences. (Running on oeis4.)