The OEIS is supported by the many generous donors to the OEIS Foundation.

 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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A076305 Numbers n such that prime(n) + prime(n+1) + prime(n+2) is a square. 10
 6, 12, 59, 65, 112, 965, 1029, 1455, 1706, 1830, 1890, 2573, 3457, 4490, 4664, 5609, 7927, 9130, 10078, 10143, 12597, 18248, 19727, 20086, 20887, 21708, 22739, 25041, 26536, 28511, 29346, 29664, 29774, 33387, 39945, 40677, 46136, 49869, 58135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A076304 for the square roots of the sums of the three primes. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..600 FORMULA a(n) = A000720(A206279(n)). - M. F. Hasler, Jan 03 2020 EXAMPLE 6 is in the sequence because prime(6) + prime(7) + prime(8) = 13 + 17 + 19 = 49 = 7^2. MATHEMATICA Select[Range[60000], IntegerQ[Sqrt[Sum[Prime[k], {k, #, # + 2}]]] &] (* Ray Chandler, Sep 26 2006 *) Position[Partition[Prime[Range[60000]], 3, 1], _?(IntegerQ[Sqrt[ Total[ #]]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, Sep 28 2018 *) PROG (PARI) n=0; p=2; q=3; forprime(r=5, 1e9, n++; if(issquare(p+q+r), print1(n", ")); p=q; q=r) \\ Charles R Greathouse IV, Apr 07 2017 (Magma) [k:k in [1..60000]| IsSquare(&+[NthPrime(k+m):m in [0, 1, 2]])]; // Marius A. Burtea, Jan 04 2020 CROSSREFS Cf. A076304 (square roots of sums), A080665 (squares = sums), A206279 (lesser of the primes). Cf. A064397 (same for 2 primes), A072849 (4 primes), A166255 (70 primes), A166261 (120 primes). Sequence in context: A076722 A322288 A337739 * A088944 A335000 A352806 Adjacent sequences: A076302 A076303 A076304 * A076306 A076307 A076308 KEYWORD nonn AUTHOR Zak Seidov, Oct 05 2002 EXTENSIONS Corrected by Ray Chandler, Sep 26 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 08:24 EST 2022. Contains 358649 sequences. (Running on oeis4.)