A339953 Primes of the form (p + 2*q + r)/6 where p, q and r are consecutive primes.

5, 7, 11, 13, 29, 47, 67, 71, 73, 83, 131, 151, 233, 307, 461, 467, 479, 571, 577, 587, 613, 619, 643, 727, 853, 947, 953, 967, 991, 1063, 1093, 1231, 1249, 1291, 1297, 1427, 1489, 1493, 1867, 1871, 1879, 2017, 2083, 2111, 2251, 2309, 2311, 2473, 2749, 2753, 2767, 3011, 3089, 3191, 3313, 3691

Offset

1,1

Links

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

Formula

a(n) = (A151799(A339954(n))+2*A339954(n)+A151800(A339954(n)))/6.

Example

a(3) = 11 is a term because 13, 17, 19 are consecutive primes with (13+2*17+19)/6 = 11 and 11 is prime.

Maple

q:= 2: r:= 3:
count:= 0: R:= NULL:
while count < 100 do
   p:= q; q:= r; r:= nextprime(r);
   w:= (p+2*q+r)/6;
   if w::integer and isprime(w) then
    count:= count+1; R:= R, w;
   fi
od:
R;

Crossrefs

Cf. A151799, A151800, A339954.

Sequence in context: A265006 A135930 A163429 * A220951 A136055 A250127

Adjacent sequences: A339950 A339951 A339952 * A339954 A339955 A339956

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 24 2020

Status

approved