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!)
A288632 Primes p such that (p+q)/6 is prime, q is the next prime after p. 2
5, 7, 13, 19, 37, 67, 89, 109, 127, 307, 379, 389, 449, 487, 499, 683, 719, 769, 877, 929, 937, 1009, 1163, 1297, 1523, 1559, 1567, 1831, 1933, 1979, 2153, 2213, 2221, 2269, 2389, 2459, 2659, 2803, 2857, 2909, 3037, 3089 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Among first 2*10^6 primes there are 61953 terms of the sequence; e.g., a(60000)=31320053 and (31320053+31320061)/6=10440019=A000040(691876).

Except for the case 7-5=2 the minimal value of first differences is 4.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000

EXAMPLE

5+7=6*2, 7+11=6*3, 13+17=6*5, 19+23=6*7, 37+41=6*11, 67+71=6*23.

MAPLE

P:=proc(n) local a, b; a:=ithprime(n); b:=(a+nextprime(a))/6; if type(b, integer) then if isprime((ithprime(n)+ithprime(n+1))/6) then a; fi; fi; end: seq(P(i), i=1..10^3); # Paolo P. Lava, Jun 13 2017

MATHEMATICA

Select[Prime[Range[1000]], PrimeQ[(# + NextPrime[#])/6] &]

CROSSREFS

Cf. A000040, A001043.

Sequence in context: A072677 A117249 A063910 * A189557 A045444 A129782

Adjacent sequences:  A288629 A288630 A288631 * A288633 A288634 A288635

KEYWORD

nonn

AUTHOR

Zak Seidov, Jun 12 2017

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 May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)