The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 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!)
 A261655 Squares equal to the difference between two successive primes of the form k^2+2 in the order in which they appear in A056899. 2
 1, 144, 1296, 3600, 176400, 156816, 2985984, 921600, 2702736, 11696400, 18974736, 21566736, 17740944, 5992704, 125888400, 7290000, 8363664, 12027024, 63680400, 210830400, 13838400, 72590400, 15116544, 15397776, 67568400, 128595600, 80784144, 93315600, 33039504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Note that all terms after the first are divisible by 144: for n>1 the sequence b(n) = sqrt(a(n)/144) is 1, 3, 5, 35, 33, 144, 80, 137, 285, 363, 387, 351, 204, 935, 225, 241, 289, ..., see A261659. The proof that all terms are == 0 (mod 144) is simple once you realize that the primes == 11 (mod 72), see comment in A056899. - Robert G. Wilson v, Sep 03 2015 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..1100 EXAMPLE A056899(2)- A056899(1) = 3-2 = 1^2; A056899(5)- A056899(4) = 227-83 = 144 = 12^2; A056899(14)- A056899(13) = 12323-11027 = 1296 = 36^2. MAPLE q:=2:for n from 1 to 10^7 do:p:=n^2+2:if isprime(p) then x:=p-q:q:=p: z:=sqrt(x):if z=floor(z) then printf(`%d, `, x):else fi:fi:od: MATHEMATICA Select[ Differences[ Select[ Range[0, 1000000], PrimeQ[#^2 + 2] &]^2], IntegerQ@ Sqrt@# &] (* or *) k = 1; p = 3; lst = {1}; While[k < 10000001, q = (6k +3)^2 + 2; If[ PrimeQ@ q, If[ IntegerQ@ Sqrt[q - p], AppendTo[lst, q - p]]; p = q]; k++] (* Robert G. Wilson v, Sep 03 2015 *) CROSSREFS Cf. A056899, A216330, A261659. Sequence in context: A133062 A211473 A203826 * A203819 A222515 A023096 Adjacent sequences:  A261652 A261653 A261654 * A261656 A261657 A261658 KEYWORD nonn AUTHOR Michel Lagneau, Aug 28 2015 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.

Last modified December 5 11:05 EST 2021. Contains 349557 sequences. (Running on oeis4.)