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A105019 Smallest prime of just n consecutive primes all of which are irregular. 2
37, 101, 461, 283, 607, 2357, 13693, 15733, 149969, 22283, 8597, 2580511, 2111491, 670619, 13326493, 92590969, 926790421, 216001147 (list; graph; refs; listen; history; text; internal format)
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 * A090496 A005107 A139934

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

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Last modified May 23 07:08 EDT 2019. Contains 323508 sequences. (Running on oeis4.)