OFFSET
1,2
COMMENTS
From Ahmad J. Masad, Dec 09 2019: (Start)
Conjecture 1: This sequence is infinite.
Conjecture 2: If this sequence is infinite, then for each prime number p > 2, there exists a minimum sufficiently large number k such that all terms >= k are multiples of p. (End)
Apparently, all terms >= 90 are multiples of 15. - Hugo Pfoertner, Dec 09 2019
Positions of records in A045917. - Sean A. Irvine, Dec 04 2021
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..266 (terms < 10^7)
EXAMPLE
a(1) = 1: average of 0 pairs of primes;
a(2) = 2: average of 1 pair of primes (2,2);
a(3) = 5: average of 2 pairs of primes (3,7), (5,5);
a(4) = 11: average of 3 pairs of primes (3,19), (5,17), (11,11);
a(5) = 17: average of 4 pairs of primes (3,31), (5,29), (11,23), (17,17).
MAPLE
(for n>0): printlevel := -1:maxx := 0:for j from 2 to 1000 do count := 0; for k from 0 to j-2 do if (isprime(j-k) and isprime(j+k)) then count := count+1 fi od; if count>maxx then print(j, count); maxx := count fi od;
CROSSREFS
KEYWORD
nonn
AUTHOR
Len Smiley, Feb 23 2000
EXTENSIONS
More terms from James A. Sellers, Feb 25 2000
STATUS
approved