A160920 Primes which are at the same time balanced primes of order 2, 3 and 4.

236429, 1108477, 1829801, 2073263, 2191513, 2192789, 3236267, 3990031, 4248947, 4485683, 4986061, 6869969, 7711079, 8473811, 8480911, 9282173, 9327277, 9350123, 9547303, 9730649, 12077909, 12993917, 13165441, 13398611, 14129761, 14785907

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 30 2009

Keywords

• nonn

Comments

The intersection of A082077, A082078 and A082079.

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..200
• Wikipedia, Balanced prime

Crossrefs

Cf. A040040, A051795, A082077, A082078, A082079.

Programs

GAP

P:=Filtered([1,3..2*10^7+1],IsPrime);;
a:=Intersection(List([2,3,4],b->List(Filtered(List([0..Length(P)-(2*b+1)],k->List([1..2*b+1],j->P[j+k])),i->Sum(i)/(2*b+1)=i[b+1]),m->m[b+1]))); # Muniru A Asiru, Apr 08 2018

Maple

isBalPr := proc(p,o) local r,s,i ; r := p ; if isprime(p) then s := p ; for i from 1 to o do r := nextprime(r) ; s := s+r ; end do: r := p ; for i from 1 to o do r := prevprime(r) ; s := s+r ; end do: s := s/(2*o+1) ; if s = p then true; else false; end if; else false; end if; end proc:
isA160920 := proc(p) isBalPr(p,2) and isBalPr(p,3) and isBalPr(p,4) ; end proc:
for i from 10 do p := ithprime(i) ; if isA160920(p) then printf("%d,\n",p); end if; end do: # R. J. Mathar, Dec 15 2010

Mathematica

PrimeNext[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k],k++ ];k];PrimePrev[n_]:=Module[{k},k=n-1;While[ !PrimeQ[k],k-- ];k];lst={};Do[p=Prime[n];a1=PrimePrev[p];a2=PrimePrev[a1];a3=PrimePrev[a2];a4=PrimePrev[a3];a5=PrimePrev[a4];b1=PrimeNext[p];b2=PrimeNext[b1];b3=PrimeNext[b2];b4=PrimeNext[b3];b5=PrimeNext[b4];If[(a1+a2+a3+a4+b1+b2+b3+b4)/8==p&&(a1+a2+a3+b1+b2+b3)/6==p&&(a1+a2+b1+b2)/4==p,AppendTo[lst,p]],{n,2*9!}];lst