A270696 Perfect powers that are the average of two consecutive primes.

4, 9, 64, 81, 144, 225, 324, 441, 625, 1089, 1681, 1728, 2601, 3600, 4096, 5184, 6084, 8464, 12544, 13689, 16641, 17576, 19044, 19600, 21952, 25281, 27225, 28224, 29584, 36864, 38025, 39204, 45369, 46656, 47524, 51984, 56169, 74529, 87025, 88804, 91809, 92416, 95481

Offset

1,1

Comments

The corresponding lesser primes are in A242380. - Michel Marcus, Mar 23 2016

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

1728 is a term because 1728 = 12^3 = (1723 + 1733)/2.

Mathematica

Select[Mean/@Partition[Prime[Range[10000]], 2, 1], GCD@@FactorInteger[#][[All, 2]]>1&] (* Harvey P. Dale, Jun 22 2022 *)

Prog

(PARI) for(n=2, 1e5, if((nextprime(n) - n) == (n - precprime(n)) && ispower(n), print1(n, ", ")));
(PARI) list(lim)=my(v=List(), t); forprime(e=2, logint(lim\=1, 2), for(m=2, sqrtnint(lim, e), t=m^e; if(t-precprime(t)==nextprime(t)-t, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 21 2016

Crossrefs

Cf. A001597, A024675, A242380.

Sequence in context: A217854 A369866 A028822 * A069495 A029788 A062826

Adjacent sequences: A270693 A270694 A270695 * A270697 A270698 A270699

Keyword

nonn

Author

Altug Alkan, Mar 21 2016

Status

approved