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A160920
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Primes which are at the same time balanced primes of order 2, 3 and 4.
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1
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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MAPLE
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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
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MATHEMATICA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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