login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A215719 The smallest of four consecutive primes with prime gaps {a,b,c} = {10,18,2}. 1
1249, 14293, 17929, 31741, 32089, 33151, 35869, 57193, 60859, 64891, 71443, 85303, 87481, 90793, 93103, 98533, 99679, 99961, 108079, 131221, 135319, 139429, 140731, 144451, 157639, 165559, 171439, 175909, 180043, 186619, 193153, 203353, 214531, 217489 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: The terms of any feasible prime gap triple {a,b,c} to form a quadruple of consecutive primes are sums of terms of three consecutive subsequences of the infinite integer sequence with period (4,2,4,2,4,6,2,6). By this token all possible sequences of quadruples of consecutive primes can be generated, including those already in the OEIS.

LINKS

Robert Israel, Table of n, a(n) for n = 1..4147

EXAMPLE

The terms of the prime gap triple {10,18,2} are the sums of the terms of the following (arbitrarily chosen) subsequences ..., {4,2,4}, {6,2,6,4}, {2}, ... For n=3, a(n) = 17929 is the smallest prime of the third prime quadruple {17929, 17939, 17957, 17959}.

MAPLE

N:= 10^6; # to get all terms <= 6*N

Primes1:= select(isprime, {seq(6*i+1, i=1..N+5)}):

Primes5:= select(isprime, {seq(6*i+5, i=1..N+5)}):

Q:= `intersect`(Primes1, map(t->t-10, Primes5), map(t->t-28, Primes5), map(t->t-30, Primes1):

A215719:= select(t -> select(isprime, {seq(t+2*i, i=1..13)}) = {t+10}, Q): # Robert Israel, May 04 2014

CROSSREFS

Cf. A078858.

Sequence in context: A233222 A020384 A086709 * A120376 A231805 A122272

Adjacent sequences:  A215716 A215717 A215718 * A215720 A215721 A215722

KEYWORD

nonn

AUTHOR

V.J. Pohjola, Aug 22 2012

EXTENSIONS

Definition and comment corrected by Robert Israel, May 04 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 3 13:53 EDT 2020. Contains 333197 sequences. (Running on oeis4.)