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A113875
Slowest growing sequence of primes having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime.
5
3, 7, 19, 139, 859, 8179, 173059, 1026199, 1827139, 15828679, 13187242759, 18732483199, 912492556939, 9130567625119
OFFSET
1,1
COMMENTS
Assuming the prime k-tuples conjecture, Granville shows (in section 2.4) that this sequence is infinite.
LINKS
Andrew Granville, Prime number patterns, The American Mathematical Monthly, Vol. 115, No. 4 (2008), pp. 279-296; alternative link.
FORMULA
a(n) = 2*A119751(n)+1. - Don Reble, Aug 17 2021
EXAMPLE
The pairwise averages of {3,7,19} are the primes {5,11,13}.
MATHEMATICA
s={3, 7}; i=5; Do[While[ !And@@PrimeQ[(s+Prime[i])/2], i++ ]; AppendTo[s, Prime[i]]; i++, {n, 3, 10}]; s
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
T. D. Noe, Jan 26 2006
EXTENSIONS
More terms from Don Reble and Giovanni Resta, Feb 15 2006
a(14) from Amiram Eldar, Jun 27 2024
STATUS
approved