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

1,1

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

Links

Table of n, a(n) for n=1..18.

Example

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.

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}]

Crossrefs

Cf. A000928, A105018.

Sequence in context: A130229 A142941 A176973 * A351141 A090496 A005107

Adjacent sequences: A105016 A105017 A105018 * A105020 A105021 A105022

Keyword

nonn,more

Author

Robert G. Wilson v, Mar 31 2005

Extensions

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

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

Status

approved