A096215 -id:A096215 - cp's OEIS frontend

A099655 a[n]=A098085[n]-A096215[n], difference between next and previous primes to A011974[n], the sum of two consecutive primes.

4, 4, 2, 2, 6, 2, 6, 2, 6, 2, 4, 6, 6, 8, 4, 4, 14, 4, 2, 10, 6, 6, 6, 10, 2, 12, 12, 12, 12, 2, 6, 6, 6, 10, 14, 4, 14, 14, 10, 4, 8, 6, 6, 8, 8, 10, 6, 8, 8, 2, 12, 8, 8, 6, 12, 18, 18, 10, 6, 6, 6, 2, 2, 12, 12, 6, 12, 8, 10, 8, 10, 8, 4, 6, 8, 4, 14, 12, 2, 2, 14, 14, 14, 14, 2, 20, 20, 8, 10, 8

Offset: 1

Labos Elemer, Nov 17 2004

nonn

			n=8, p(8)+p(9)=19+23=42,a[8]=43-41=2=a(8).

Cf. A098085, A096215, A011974.

Mathematica
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<Harvey P. Dale, Mar 07 2017 *)
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a(n)=NextPrime[p(n)+p(n+1)]-PreviousPrime[p(n)+p(n+1)]

A346416 Primes p such that the greatest perimeter of a triangle with prime sides including p and the next prime is prime.

Original entry on oeis.org

5, 11, 13, 17, 19, 37, 41, 43, 47, 59, 71, 89, 103, 109, 113, 137, 139, 149, 163, 167, 173, 179, 181, 241, 269, 313, 337, 379, 389, 401, 491, 499, 521, 547, 557, 569, 587, 599, 607, 613, 617, 631, 643, 673, 677, 701, 739, 773, 787, 811, 839, 877, 883, 887, 929, 941, 953, 971, 977, 983, 1019, 1021

Offset: 1

J. M. Bergot and Robert Israel, Jul 15 2021

nonn

If p is prime and q is the next prime, the greatest perimeter is p+q+r where r is the greatest prime < p+q.

			a(3) = 13 is a term because the next prime is 17, the greatest prime < 13+17 is 29, and 13+17+29 = 59 is prime.

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

Cf. A096215.

f:= proc(n) local p,q,r,s;
  p:= ithprime(n);
  q:= ithprime(n+1);
  r:= prevprime(p+q);
  s:= p+q+r;
  if isprime(p+q+r) then return p fi
end proc:
map(f, [$1..500]);

Select[Partition[Prime[Range[200]],2,1],PrimeQ[Total[#]+NextPrime[Total[#],-1]]&][[;;,1]] (* Harvey P. Dale, Dec 11 2024 *)

cp's OEIS Frontend

A099655 a[n]=A098085[n]-A096215[n], difference between next and previous primes to A011974[n], the sum of two consecutive primes.

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