A113875 - OEIS

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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.

3, 7, 19, 139, 859, 8179, 173059, 1026199, 1827139, 15828679, 13187242759, 18732483199, 912492556939, 9130567625119

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OFFSET

1,1

COMMENTS

Assuming the prime k-tuples conjecture, Granville shows (in section 2.4) that this sequence is infinite.

LINKS

Table of n, a(n) for n=1..14.

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

Cf. A113832, A115760, A119751.

Sequence in context: A128024 A245723 A118128 * A111974 A243100 A173400

Adjacent sequences: A113872 A113873 A113874 * A113876 A113877 A113878

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