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A268480 Integers n such that A002110(n) is the average of two consecutive primes. 0
2, 3, 5, 8, 38, 40, 64, 73, 89, 236, 480, 486 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In other words, the primorial numbers that are considered are those of the form (p + q)/2 where p and q are consecutive primes. Note that the initial values of (p - q)/2 are 1, 1, 1, 23, 239, 191, 331, 373, 1021.

A088256 is a subsequence of these primorials, which in turn are a subsequence of A024675.

LINKS

Table of n, a(n) for n=1..12.

Index entries for sequences related to primorial numbers

EXAMPLE

5 is a term because 2*3*5*7*11 = 2310 = (2309 + 2311)/2.

8 is a term because 2*3*5*7*11*13*17*19 = 9699690 = (9699667 + 9699713)/2.

MAPLE

P:= 2: count:= 0:

for n from 2 to 500 do

  P:= P*ithprime(n);

  # first try d=1

  if isprime(P+1) then

    good:= isprime(P-1);

  elif isprime(P-1) then good:= false

  else

    for d from ithprime(n+1) by 2 do

      if igcd(d, P) > 1 then next fi;

      if isprime(P+d) then

        good:= isprime(P-d); break

      elif isprime(P-d) then

        good:= false; break

      fi

    od;

  fi;

  if good then

     count:= count+1;

     A[count]:= n;

  fi

od:

seq(A[i], i=1..count);  # Robert Israel, Aug 29 2016

PROG

(PARI) a002110(n) = prod(k=1, n, prime(k));

for(n=2, 1e3, if((nextprime(a002110(n)) - a002110(n)) == (a002110(n) - precprime(a002110(n))), print1(n, ", ")))

CROSSREFS

Cf. A002110, A024675, A088256.

Sequence in context: A042069 A041008 A041569 * A128485 A042471 A041871

Adjacent sequences:  A268477 A268478 A268479 * A268481 A268482 A268483

KEYWORD

nonn,more

AUTHOR

Altug Alkan, Mar 21 2016

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)