A242380 -id:A242380 - cp's OEIS frontend

A242382 Lesser of consecutive primes whose average is a perfect cube.

61, 1723, 4093, 17573, 21943, 46649, 110587, 195103, 287491, 314423, 405221, 474547, 1061189, 1191013, 1404919, 1601609, 1906621, 2000371, 2146687, 2196979, 3241783, 3511799, 4912991, 5268017, 6229501, 6751267, 6858997, 7077883, 11239421, 20346407, 21951997, 26198063

Offset: 1

Antonio Roldán, May 12 2014

nonn

			1723 is in the sequence because it is prime, nextprime(1723) = 1733, and average(1723,1733) = 1728 = 12^3.

Amiram Eldar, Table of n, a(n) for n = 1..128

Subsequence of A077037 and A242380.

Cf. A225195, A091624.

Select[Partition[Prime[Range[2, 10^5]], 2, 1], IntegerQ[Surd[(First[#] + Last[#])/2, 3]] &][[;; , 1]] (* Amiram Eldar, Jul 04 2022 *)

{for(i=3,3*10^7,if(isprime(i),k=(i+nextprime(i+1))/2;if(ispower(k,3),print1(i,", "))))}

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

Original entry on oeis.org

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

Altug Alkan, Mar 21 2016

nonn

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

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

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

Cf. A001597, A024675, A242380.

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

for(n=2, 1e5, if((nextprime(n) - n) == (n - precprime(n)) && ispower(n), print1(n, ", ")));

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

cp's OEIS Frontend

A242382 Lesser of consecutive primes whose average is a perfect cube.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

PARI