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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A252231 Primes of the form (p+q)^2 + pq, where p and q are consecutive primes. 1
31, 79, 179, 401, 719, 1619, 3371, 8819, 12491, 15671, 23801, 25919, 28871, 32801, 95219, 118571, 154871, 161999, 190121, 266801, 322571, 364499, 375371, 449951, 524831, 725801, 772229, 796001, 820109, 994571, 1026029, 1053401, 1081121, 1225109, 1326089, 1415039 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..12799

EXAMPLE

79 is in the sequence because (3+5)^2 + 3*5 = 79, which is prime.

401 is in the sequence because (7+11)^2 + 7*11 = 401, which is prime.

MAPLE

count:= 0:

p:= 2:

while count < 100 do

  q:= nextprime(p);

  x:= (p+q)^2+p*q;

  if isprime(x) then

    count:= count+1;

    a[count]:= x;

  fi;

  p:= q;

od:

seq(a[i], i=1..count); # Robert Israel, Dec 16 2014

MATHEMATICA

Select[Table[(Prime[n] + Prime[n+1])^2 + Prime[n]Prime[n+1], {n, 100}], PrimeQ[#] &]

Select[Total[#]^2+Times@@#&/@Partition[Prime[Range[100]], 2, 1], PrimeQ] (* Harvey P. Dale, Sep 06 2020 *)

PROG

(PARI) s=[]; for(k=1, 100, p=prime(k); q=prime(k+1); t=(p+q)^2 + p*q; if(isprime(t), s=concat(s, t))); s

CROSSREFS

Cf. A000040, A007645, A003136, A243761, A252017.

Sequence in context: A139855 A139901 A242777 * A044169 A044550 A055810

Adjacent sequences:  A252228 A252229 A252230 * A252232 A252233 A252234

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Dec 15 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 December 7 07:01 EST 2021. Contains 349567 sequences. (Running on oeis4.)