A105019 Smallest prime of just n consecutive primes all of which are irregular.

37, 101, 461, 283, 607, 2357, 13693, 15733, 149969, 22283, 8597, 2580511, 2111491, 670619, 13326493, 92590969, 926790421, 216001147

Offset: 1

Author

Robert G. Wilson v, Mar 31 2005

Keywords

• nonn
• more

Comments

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

Examples

			a(1)=37 because neither 31 nor 41, its neighboring primes, are irregular.
a(2)=101 because neither 97 nor 107 are irregular, they being the neighbors of 101 and 103 which are irregular.
a(3)=461 because neither 457 nor 479 are irregular, they being the neighbors of {461, 463, 467} which are all irregular.
		

Crossrefs

Cf. A000928, A105018.

Programs

Mathematica

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}]

Extensions

More terms from Robert G. Wilson v, Mar 31 2005

a(15)-a(18) from Amiram Eldar, Mar 06 2019