A341421 - OEIS

A341421

a(n) is the number of k <= n for which (prime(k)+3*prime(k+1))/2 is prime minus the number of k <= n for which (prime(k)+3*prime(k+2))/2 is prime.

0, 0, 0, -1, -2, -2, -2, -3, -3, -2, -1, -2, -2, -3, -2, -2, -2, -2, -2, -2, -2, -3, -3, -3, -3, -4, -4, -5, -5, -5, -6, -5, -4, -3, -3, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 1, 0, -1, -1, -1, -1, -1, -2, -3, -3, -3, -3, -3, -3, -4, -5, -4, -5, -6, -7

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

Although most of the first few hundred values are negative, it appears that a(n) > 0 for n > 4631.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Robert Israel, Plot of (n,a(n)) for 1 <= n <= 10^5

EXAMPLE

a(5) = -2 because for k <= 5, only (prime(3)+3*prime(4))/2 = 13 is prime while (prime(3)+3*prime(5))/2 = 19, (prime(4)+3*prime(6))/2 = 23 and (prime(5)+3*prime(7))/2 are prime.

MAPLE

A[1]:= 0: t:= 0:

for n from 2 to 1000 do

if isprime((ithprime(n)+3*ithprime(n+1))/2) then t:= t+1 fi;

if isprime((ithprime(n)+3*ithprime(n+2))/2) then t:= t-1 fi;

A[n]:= t;

od:

seq(A[i], i=1..1000);

CROSSREFS

Sequence in context: A071452 A282495 A354226 * A308890 A081414 A328577

Adjacent sequences: A341418 A341419 A341420 * A341422 A341423 A341424

KEYWORD

sign,look

AUTHOR

J. M. Bergot and Robert Israel, Apr 09 2021

STATUS

approved