VOOZH about

URL: https://oeis.org/A064397

⇱ A064397 - OEIS

login
A064397
Numbers k such that prime(k) + prime(k+1) is a square.
15
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
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)
FORMULA
a(n) = A000720(A061275(n)). - Amiram Eldar, Jun 28 2024
a(n) >> n^2/log^2 n. - Charles R Greathouse IV, Mar 08 2025
EXAMPLE
For k=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), A000720.
Cf. A076305 (3 primes), A072849 (4 primes), A166255 (70 primes), A166261 (120 primes).
Sequence in context: A298050 A115783 A140109 * A214467 A151971 A014659
KEYWORD
nonn
AUTHOR
Jason Earls, Sep 29 2001
STATUS
approved