A155128 Primes P(n) such that 2*P(n) - P(n+1) has all factors less than P(n+1) - P(n). This means that no prime less than P(n) can divide P(n) to give a remainder added to P(n) to give P(n+1).

3, 7, 13, 31, 89, 113, 131, 449, 577, 683, 743, 839, 887, 1039, 1237, 1637, 1831, 2039, 2213, 2221, 2557, 2843, 2939, 3391, 3947, 4111, 4139, 4889, 5281, 5987, 6803, 6841, 7883, 8513, 10667, 10739, 13381, 13487, 14177, 14563, 14639, 15319, 15443, 16273

Offset

1,1

Comments

These primes need not necessarily occur before a large prime gap.

Do they occur less frequently than twin primes?

Links

Table of n, a(n) for n=1..44.

Formula

Found by inspecting a table of factors and primes.

Example

For P(n)=1237 and P(n+1)=1249, 2*1237 - 1249 = 1225 = 5^2 * 7^2
and 5,7 < 1249 - 1237 = 12.

Mathematica

Join[{3}, Prime[Select[Range[3, 2000], FactorInteger[2*Prime[ # ] - Prime[ # + 1]][[ -1, 1]] < Prime[ # + 1] - Prime[ # ] &]]] (* Stefan Steinerberger, Jan 31 2009 *)

Crossrefs

Sequence in context: A126879 A247895 A336688 * A176589 A077314 A069246

Adjacent sequences: A155125 A155126 A155127 * A155129 A155130 A155131

Keyword

base,easy,nonn

Author

J. M. Bergot, Jan 20 2009

Extensions

Corrected and extended by Stefan Steinerberger, Jan 31 2009

Status

approved