A105019 - OEIS

%I #9 Mar 06 2019 20:20:16

%S 37,101,461,283,607,2357,13693,15733,149969,22283,8597,2580511,

%T 2111491,670619,13326493,92590969,926790421,216001147

%N Smallest prime of just n consecutive primes all of which are irregular.

%C The author hereby expresses his gratitude to _Tony Noe_ for supplying him with a list of the first irregular primes to 12 million. - _Robert G. Wilson v_, Mar 31 2005

%e a(1)=37 because neither 31 nor 41, its neighboring primes, are irregular.

%e a(2)=101 because neither 97 nor 107 are irregular, they being the neighbors of 101 and 103 which are irregular.

%e a(3)=461 because neither 457 nor 479 are irregular, they being the neighbors of {461, 463, 467} which are all irregular.

%t fQ[n_] := Block[{ p = Prime[ n ], k = 1}, While[ 2k <= p - 3 && Mod[ Numerator[ BernoulliB[ 2k]], p] != 0, k++ ]; If[ 2k != p - 1, True, False]]; Select[ Range[2, 250], fQ[ # ] &]; s = {}; Do[ If[ fQ[n], AppendTo[s, n]; Print[{n, Prime[n]}]], {n, 1500}]

%Y Cf. A000928, A105018.

%K nonn,more

%O 1,1

%A _Robert G. Wilson v_, Mar 31 2005

%E More terms from _Robert G. Wilson v_, Mar 31 2005

%E a(15)-a(18) from _Amiram Eldar_, Mar 06 2019