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!)
A235920 Primes p with prime(p) - p + 1 and (p^2 - 1)/4 - prime(p) both prime. 1
17, 31, 41, 43, 61, 71, 83, 103, 109, 173, 181, 211, 271, 349, 353, 541, 661, 673, 743, 811, 911, 953, 971, 1171, 1429, 1471, 1483, 1723, 1787, 2053, 2203, 2579, 2749, 3019, 3299, 3391, 3433, 3463, 3727, 3917, 4003, 4021, 4049, 4243, 4447, 4567, 4657, 4729, 4801, 4993 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By the conjecture in A235919, this sequence should have infinitely many terms.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 17 with prime(17) - 17 + 1 =   59 - 16 = 43 and (17^2 - 1)/4 - prime(17) = 72 - 59 = 13 both prime.

MATHEMATICA

PQ[n_]:=n>0&&PrimeQ[n]

p[n_]:=PrimeQ[Prime[n]-n+1]&&PQ[(n^2-1)/4-Prime[n]]

n=0; Do[If[p[Prime[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 1000}]

CROSSREFS

Cf. A000040, A234695, A235727, A235806, A235914, A235919.

Sequence in context: A333855 A321217 A095748 * A268923 A172287 A062579

Adjacent sequences:  A235917 A235918 A235919 * A235921 A235922 A235923

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 17 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 July 8 04:16 EDT 2020. Contains 335504 sequences. (Running on oeis4.)