A246401 Smallest prime number Q such that the sum prime(n)+prime(n+1)+Q is a prime number.

2, 3, 5, 5, 5, 7, 5, 5, 7, 7, 3, 5, 5, 7, 3, 19, 7, 3, 11, 5, 5, 5, 7, 5, 13, 7, 13, 7, 5, 11, 5, 3, 5, 5, 7, 3, 11, 7, 7, 7, 7, 7, 5, 7, 5, 11, 5, 7, 5, 5, 7, 7, 7, 13, 3, 31, 7, 23, 5, 5, 11, 7, 13, 7, 11, 5, 5, 7, 5, 7, 7, 7, 3, 5, 7, 37, 11, 11, 11, 11, 13

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

2+3+2=7 is prime so a(1)=2.
3+5+3=11 is prime so a(2)=3.
5+7+3=15 is composite, and 5+7+5=17 is prime so a(3)=5.

Mathematica

spn[n_]:=Module[{p=2}, While[!PrimeQ[n+p], p=NextPrime[p]]; p]; spn/@ (Total/@ Partition[Prime[Range[100]], 2, 1]) (* Harvey P. Dale, Mar 14 2022 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM k
DIM n, 0
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET n, n+1
IF n>10000 THEN END
SET k, 0
LABEL loop2
SET k, k+1
PRP p(n)+p(n+1)+p(k)
IF ISPRP then GOTO a
GOTO loop2
LABEL a
WRITE myf, t
GOTO loop1
(PARI) a(n) = t=prime(n)+prime(n+1); k=1; while(!isprime(t+q=prime(k)), k++); q \\ Colin Barker, Aug 25 2014

Crossrefs

Cf. A246400.

Sequence in context: A102642 A183228 A133304 * A003660 A065688 A348976

Adjacent sequences: A246398 A246399 A246400 * A246402 A246403 A246404

Keyword

nonn

Author

Pierre CAMI, Aug 25 2014

Status

approved