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A212820
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Balanced primes which are the average of two successive semiprimes.
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2
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5, 53, 173, 211, 1511, 3307, 3637, 4457, 4993, 6863, 11411, 11731, 11903, 12653, 15907, 18223, 20107, 20201, 20347, 20731, 22051, 23801, 26041, 35911, 39113, 40493, 46889, 47303, 51551, 52529, 60083, 63559, 69623, 71011, 75787, 77081, 78803, 85049, 91297
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OFFSET
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1,1
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COMMENTS
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Prime p which is the average of the previous prime and the following prime and is also the average of two successive semiprimes.
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LINKS
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FORMULA
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EXAMPLE
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53 is in the sequence because it is the average of 47 and 59 (the two neighboring primes) and 51 and 55 (the two neighboring semiprimes).
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MAPLE
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with(numtheory):
prevsp:= proc(n) local k; for k from n-1 by -1
while isprime(k) or bigomega(k)<>2 do od; k end:
nextsp:= proc(n) local k; for k from n+1
while isprime(k) or bigomega(k)<>2 do od; k end:
a:= proc(n) option remember; local p;
p:= `if`(n=1, 2, a(n-1));
do p:= nextprime(p);
if p=(prevprime(p)+nextprime(p))/2 and
p=(prevsp(p)+nextsp(p))/2 then break fi
od; p
end:
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MATHEMATICA
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prevsp[n_] := Module[{k}, For[k = n-1, PrimeQ[k] || PrimeOmega[k] != 2, k--]; k];
nextsp[n_] := Module[{k}, For[k = n+1, PrimeQ[k] || PrimeOmega[k] != 2 , k++]; k];
a[n_] := a[n] = Module[{p}, p = If[n==1, 2, a[n-1]]; While[True, p = NextPrime[p]; If[p == (NextPrime[p, -1] + NextPrime[p])/2 && p == (prevsp[p] + nextsp[p])/2, Break[]]]; p];
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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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