A299644 -id:A299644 - cp's OEIS frontend

A098042 Primes of the form (prime(prime(k)) + prime(prime(k+1)))/2.

307, 593, 1459, 1511, 1609, 2399, 2447, 2579, 2903, 4409, 5953, 6317, 7151, 11083, 12491, 14753, 16067, 18199, 18223, 20929, 21787, 23893, 25667, 26317, 31051, 37139, 37573, 37871, 40283, 40471, 41201, 41479, 42013, 44537, 44741, 48409

Offset: 1

Cino Hilliard, Sep 10 2004

Primes of the form A299644(k)/2. - Amiram Eldar, Jul 08 2024

			prime(prime(18)) = 283, prime(prime(19)) = 331. (283 + 331)/2 = 614/2 = 307.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A006450, A098043, A299644.

With[{t = Table[Prime[Prime[n]], {n, 1, 400}]}, Select[(Most[t] + Rest[t])/2, PrimeQ]] (* Amiram Eldar, Jul 08 2024 *)

lista(n) = for(x=1,n,y=prime(prime(x+1))+prime(prime(x)); if(y%2==0&isprime(y/2),print1(y\2",")))

Offset corrected by Amiram Eldar, Jul 08 2024

A378677 a(n)=a(n-1) + prime(n) for n prime, and a(n)=-a(n-1) otherwise, with a(0)=0, with duplicates removed afterwards.

Original entry on oeis.org

0, 3, 8, -8, -3, 14, -14, 17, -17, 24, -24, 35, -35, 32, -32, 51, -51, 58, -58, 69, -69, 88, -88, 91, -91, 100, -100, 111, -111, 130, -130, 147, -147, 136, -136, 195, -195, 158, -158, 209, -209, 192, -192, 239, -239, 222, -222, 287, -287, 260, -260, 303, -303

Offset: 0

Bill McEachen, Dec 03 2024

sign

Let b = subset of positive terms for n>4. We have A073131= b(m+2)-b(m) , A006450= b(m+2)+b(m) and A299644= b(m+2)+2*b(m+1)+b(m).

			n=1 is not prime, so a(1)= -a(0)= 0. n=2 is prime, so a(2)=a(1)+prime(2)=0+3=3. n=5 is prime, so a(5)=3, but note that it duplicates a(2). n=6 is not prime, so a(6)= -a(5)=-3. After terms are computed, duplicates are only then removed, which will alter indices accordingly.

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A006450, A073131, A299644.

Module[{n = 0}, DeleteDuplicates[NestList[If[PrimeQ[++n], # + Prime[n], -#] &, 0, 200]]] (* Paolo Xausa, Dec 06 2024 *)

a(n) = a(n-1) + a prime for n odd >4.

a(n) = -a(n-1) for a(n-1)>0, n>1.

cp's OEIS Frontend

A098042 Primes of the form (prime(prime(k)) + prime(prime(k+1)))/2.

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