A113875 Slowest growing sequence of primes having the prime-pairwise-average property: if i

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

Offset: 1

Author

T. D. Noe, Jan 26 2006

Keywords

• nonn
• hard
• more

Comments

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

Examples

			The pairwise averages of {3,7,19} are the primes {5,11,13}.
		

Links

• Andrew Granville, Prime number patterns, The American Mathematical Monthly, Vol. 115, No. 4 (2008), pp. 279-296; alternative link.

Crossrefs

Cf. A113832, A115760, A119751.

Programs

Mathematica

s={3, 7}; i=5; Do[While[ !And@@PrimeQ[(s+Prime[i])/2], i++ ]; AppendTo[s, Prime[i]]; i++, {n, 3, 10}]; s

Formula

a(n) = 2*A119751(n)+1. - Don Reble, Aug 17 2021

Extensions

More terms from Don Reble and Giovanni Resta, Feb 15 2006

a(14) from Amiram Eldar, Jun 27 2024