

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).


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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
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OFFSET

1,1


COMMENTS

These primes need not necessarily occur before a large prime gap.
Do they occur less frequently than twin primes?


LINKS



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



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



