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!)
A082079 Balanced primes of order four. 19
491, 757, 1787, 3571, 6337, 6451, 6991, 7741, 7907, 8821, 10141, 10267, 10657, 12911, 15299, 16189, 18223, 18701, 19801, 19843, 19853, 19937, 21961, 22543, 22739, 22807, 23893, 23909, 24767, 25169, 25391, 26591, 26641, 26693, 26713 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The arithmetic mean of 8 primes in its "neighborhood"; not to be confused with 'Quadruply balanced primes' (A096710).
A balanced prime of order four is not necessarily balanced (A006562) order one, or of order two (A082077), or of order three (A082078), etc.
LINKS
EXAMPLE
p = 491 = {463 + 467 + 479 + 487 + 491 + 499 + 503 + 509 + 521)/9 = 4419/9.
MATHEMATICA
Do[s3=Prime[n]+Prime[n+1]+Prime[n+2]; s5=Prime[n-1]+s3+Prime[n+3]; s7=Prime[n-2]+s5+Prime[n+4]; s9=Prime[n-3]+s7+Prime[n+5]; If[Equal[s9/9, Prime[n+1]], Print[Prime[n+1]]], {n, 4, 10000}]
(* Second program: *)
With[{k = 4}, Select[MapIndexed[{Prime[First@ #2 + k], #1} &, Mean /@ Partition[Prime@ Range[3000], 2 k + 1, 1]], SameQ @@ # &][[All, 1]]] (* Michael De Vlieger, Feb 15 2018 *)
Select[Partition[Prime[Range[3000]], 9, 1], Mean[#]==#[[5]]&][[;; , 5]] (* Harvey P. Dale, Mar 09 2023 *)
PROG
(GAP) P:=Filtered([1..50000], IsPrime);;
a:=List(Filtered(List([0..3000], k->List([5..13], j->P[j-4+k])), i-> Sum(i)/9=i[5]), m->m[5]); # Muniru A Asiru, Feb 14 2018
(PARI) isok(p) = {if (isprime(p), k = primepi(p); if (k > 4, sum(i=k-4, k+4, prime(i)) == 9*p; ); ); } \\ Michel Marcus, Mar 07 2018
CROSSREFS
Sequence in context: A060975 A180457 A271664 * A260925 A217118 A205200
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 08 2003
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 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)