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A154494
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a(n+1) -+ a(n) = prime, a(n+1)*a(n) = average of twin prime pairs, a(1)=1, a(2)=6.
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8
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1, 6, 17, 84, 247, 300, 341, 720, 767, 834, 913, 960, 989, 1590, 1741, 2772, 2945, 3102, 3451, 3540, 3563, 4020, 4159, 4812, 5431, 5700, 6131, 6192, 6245, 8586, 9373, 10056, 10163, 10314, 10543, 10944, 11033, 11844, 12055, 13566, 14015, 15048, 15155
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OFFSET
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1,2
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COMMENTS
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Sum and difference of any of two consecutive numbers in current sequence are prime numbers and multiplication and any two consecutive numbers is Average of twin prime pairs : 6-1=5; 6+1=7; 6*1=6, 17-6=11; 17+6=23; 17*6=102, ... .
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LINKS
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MAPLE
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f:= proc(x) local k;
for k from x+1 by 2 do
if isprime(k+x) and isprime(k-x) and isprime(k*x-1) and isprime(k*x+1) then return k fi
od;
end proc:
R:= 1, 6: x:= 6:
for count from 3 to 100 do
x:= f(x);
R:= R, x
od:
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MATHEMATICA
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a=1; b=6; lst={a, b}; Do[If[PrimeQ[n-b]&&PrimeQ[n+b]&&PrimeQ[n*b-1]&&PrimeQ[n*b+1], AppendTo[lst, n]; a=b; b=n], {n, b+1, 9!}]; lst
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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