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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A064397 Numbers n such that prime(n) + prime(n+1) is a square. 13
7, 15, 20, 61, 152, 190, 293, 377, 492, 558, 789, 919, 942, 1768, 2343, 2429, 2693, 2952, 3136, 3720, 4837, 5421, 5722, 6870, 7347, 8126, 8193, 9465, 9857, 9927, 10410, 10483, 10653, 12685, 13763, 13955, 16033, 16342, 17859, 18367, 18474 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Zak Seidov, Table of n, a(n) for n=1..1000

EXAMPLE

n=15: prime(15) = 47 and prime(16) = 53, 47 + 53 = 100 = 10^2.

MATHEMATICA

lst={}; Do[p1=Prime[n]; p2=Prime[n+1]; q=(p1+p2)^0.5; If[q==IntegerPart[q], AppendTo[lst, n]], {n, 1, 9!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 02 2008 *)

PROG

(PARI) j=[]; for(n=1, 30000, x=prime(n)+prime(n+1); if(issquare(x), j=concat(j, n))); j

(PARI) { n=0; default(primelimit, 8500000); for (m=1, 10^9, if (issquare(prime(m) + prime(m + 1)), write("b064397.txt", n++, " ", m); if (n==175, break)) ) } \\ Harry J. Smith, Sep 13 2009

(MAGMA) [n: n in [0..50000]| IsSquare(NthPrime(n) +NthPrime(n+1))]; // Vincenzo Librandi, Apr 06 2011

CROSSREFS

Cf. A061275 (the primes), A062703 (squares), A074924 (square root of sum).

Cf. A076305 (3 primes), A072849 (4 primes), A166255 (70 primes), A166261 (120 primes).

Sequence in context: A298050 A115783 A140109 * A214467 A151971 A014659

Adjacent sequences:  A064394 A064395 A064396 * A064398 A064399 A064400

KEYWORD

nonn

AUTHOR

Jason Earls, Sep 29 2001

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 November 27 14:10 EST 2020. Contains 338683 sequences. (Running on oeis4.)