login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A126554 Arithmetic mean of two consecutive balanced primes (of order one). 7
29, 105, 165, 192, 234, 260, 318, 468, 578, 600, 630, 693, 840, 962, 1040, 1113, 1155, 1205, 1295, 1439, 1629, 1750, 1830, 2097, 2352, 2547, 2790, 2933, 3135, 3310, 3475, 3685, 3873, 4211, 4433, 4527, 4627, 4674, 4842, 5050, 5110, 5208, 5345, 5390, 5478 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Might be called interprimes of order two, since the arithmetic means of two consecutive odd primes (A024675) sometimes are called interprimes.
Balanced primes of order two (A082077) and doubly balanced primes (A051795) have different definitions.
For primes in this sequence (prime interprimes of order two) see A126555.
LINKS
Muniru A Asiru and Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Muniru A Asiru)
FORMULA
a(n) = (A006562(n+1)+A006562(n))/2.
MATHEMATICA
b = {}; a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1, 1000}]; Do[AppendTo[b, (a[[k + 1]] + a[[k]])/2], {k, 1, Length[a] - 1}]; b
PROG
(PARI) {m=6000; a=0; p=2; q=3; r=5; while(r<=m, if((p+r)/2==q, if(a>0, print1((a+q)/2, ", ")); a=q); p=q; q=r; r=nextprime(r+1))} \\ Klaus Brockhaus, Jan 05 2007
(GAP) P:=Filtered([1..6000], IsPrime);; P1:=List(Filtered(List([0..Length(P)-3], k->List([1..3], j->P[j+k])), i->Sum(i)/3=i[2]), m->m[2]);;
a:=List([1..Length(P1)-1], n->(P1[n+1]+P1[n])/2); # Muniru A Asiru, Mar 31 2018
CROSSREFS
Sequence in context: A142138 A341550 A009435 * A258721 A009406 A211496
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 27 2006
EXTENSIONS
Edited by Klaus Brockhaus, Jan 05 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)