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 A268480 Integers k such that A002110(k) 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. Numbers k such that A038711(k) = A060270(k). - Amiram Eldar, May 19 2024 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 MATHEMATICA prim[n_] := Times @@ Prime[Range[n]]; Select[Range[2, 100], Total[NextPrime[(p = prim[#]), {-1, 1}]] == 2*p &] (* Amiram Eldar, May 19 2024 *) 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, A038711, A060270, 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 July 15 06:58 EDT 2024. Contains 374324 sequences. (Running on oeis4.)