A064076 -id:A064076 - cp's OEIS frontend

A064077 Greater of odd twin prime powers (lesser = A064076).

5, 7, 9, 11, 13, 19, 25, 27, 29, 31, 43, 49, 61, 73, 81, 83, 103, 109, 127, 139, 151, 169, 181, 193, 199, 229, 241, 243, 271, 283, 313, 349, 361, 421, 433, 463, 523, 571, 601, 619, 643, 661, 729, 811, 823, 829, 841, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153

Offset: 1

Reinhard Zumkeller, Sep 01 2001

nonn

A006512 is a proper subsequence of this sequence (as A001359 is of A064076).

			a(16) = 83^1 and 83 - 1 = 81 = 3^4 = A064076(16); a(20) = 139^1 and 139 - 2 = 137^1 = A064077(20).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A064076, A000961, A006512, A061345.

Select[Partition[Select[Range[1, 1200, 2], PrimePowerQ], 2, 1], Differences[#] == {2} &][[;; , 2]] (* Amiram Eldar, Mar 19 2025 *)

a(n) = A064076(n) + 2. - Amiram Eldar, Mar 19 2025

A120431 Numbers k such that k and k+2 are prime powers.

Original entry on oeis.org

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

Offset: 1

Greg Huber, Jul 13 2006

nonn

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)

			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).

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1270 from Daniel Forgues)

Cf. A001359, A000961, A064076.

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

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

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

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

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

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

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

cp's OEIS Frontend

A064077 Greater of odd twin prime powers (lesser = A064076).

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