A110586 Squares of the form 6p+7 for p prime (A110015) that are squares of a prime.

25, 49, 121, 289, 361, 841, 1369, 1849, 2209, 2809, 3721, 5041, 5329, 6241, 7921, 9409, 10201, 11449, 11881, 16129, 29929, 36481, 39601, 49729, 58081, 63001, 69169, 73441, 78961, 100489, 134689, 151321, 157609, 187489, 192721, 196249, 201601

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Formula

a(n) = A110587(n)^2. - Amiram Eldar, Aug 02 2024

Example

a(4) = 289 since 289 = 17^2 and 289 = 6*47 + 7.

Maple

ispower := proc(n, b) andmap(proc(w) evalb(w[2] mod b = 0) end, ifactors(n)[2]) end: a:=6: PW6:=[]: for z from 1 to 1 do for n from 1 to 10000 do p:=ithprime(n); m:=a*p+a+1; if ispower(m, 2) and isprime(sqrt(m)) then PW6:=[op(PW6), m] fi od; od;

Mathematica

Select[Prime[Range[100]]^2, PrimeQ[(#-7)/6]&] (* Harvey P. Dale, May 09 2012 *)

Prog

(PARI) list(lim)=my(v=List(), p); forprime(q=5, sqrtint(lim\1*6+7), if(isprime(p=(q^2-7)/6), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Sep 20 2016

Crossrefs

Cf. A110014, A110015, A110016, A110587.

Sequence in context: A358060 A131706 A110015 * A046949 A137659 A020325

Adjacent sequences: A110583 A110584 A110585 * A110587 A110588 A110589

Keyword

nonn,easy

Author

Walter Kehowski, Sep 13 2005

Status

approved