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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-Fran├žois 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 September 15 12:22 EDT 2019. Contains 327078 sequences. (Running on oeis4.)