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 A212820 Balanced primes which are the average of two successive semiprimes. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Prime p which is the average of the previous prime and the following prime and is also the average of two successive semiprimes. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 FORMULA { A212820 } = { A006562 } intersection { A103654 }. EXAMPLE 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). MAPLE 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: seq (a(n), n=1..40);  # Alois P. Heinz, Jun 03 2012 MATHEMATICA 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]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 24 2017, after Alois P. Heinz *) CROSSREFS Cf. A006562, A103654. Sequence in context: A094847 A001992 A139899 * A094849 A094852 A267543 Adjacent sequences:  A212817 A212818 A212819 * A212821 A212822 A212823 KEYWORD nonn AUTHOR Gerasimov Sergey, May 28 2012 STATUS approved

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Last modified May 13 12:16 EDT 2021. Contains 343839 sequences. (Running on oeis4.)