|
| |
|
|
A115760
|
|
Slowest growing sequence of numbers having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime.
|
|
8
|
|
|
|
3, 7, 19, 55, 139, 859, 2119, 112999, 333679, 10040119, 15363619, 548687179, 16632374359, 5733638351299, 14360489685499, 433098704482699, 44258681327079259, 5009018648920510999
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Inspired by A113875 (case of prime numbers). See A113832 minimal sets of primes having the P-P-A property, A115782 primes in A115760.
Equals 2*A103828(n) + 1. - N. J. A. Sloane, Apr 28 2007. This sequence is surely infinite - see comments in A103828.
After a(4), terms are == 19 mod 60. The sequence may also be defined by "a(1)=3 and for n>1, a(n) is the smallest number of the form 4k+3, a(n)>a(n-1) such that the pairwise sums of all elements are semiprimes." - Don Reble, Aug 17 2021
|
|
|
LINKS
|
Table of n, a(n) for n=1..18.
|
|
|
FORMULA
|
a(n) == 19 (mod 60) for n>4 [consequence of mod 30 congruence of A103828(n).] - Don Reble, Aug 17 2021
|
|
|
EXAMPLE
|
The pairwise averages of {3,7,19} are the primes {5,11,13}.
|
|
|
CROSSREFS
|
Cf. A113832, A113875, A115782, A175532.
Sequence in context: A183122 A104522 A351633 * A175533 A183115 A183120
Adjacent sequences: A115757 A115758 A115759 * A115761 A115762 A115763
|
|
|
KEYWORD
|
more,nonn
|
|
|
AUTHOR
|
Zak Seidov, Jan 30 2006
|
|
|
EXTENSIONS
|
More terms from Don Reble and Giovanni Resta, Feb 15 2006
More terms from Don Reble, Aug 17 2021
|
|
|
STATUS
|
approved
|
| |
|
|
