|
%I #22 Sep 02 2015 12:23:06
%S 41399193,195157536843,548699719043,3036956318943,320218213825307,
%T 4132518238158443,4519695415117057,6270713759856601,18507175540175893,
%U 29390150965410193,106799085933816293,183320084770933043,220070939141434093,481373412121678901
%N Numbers with 4 prime factors a < b < c < d such that 2c = a^4 + b^2 and 2d = b^4 + c^2.
%C This sequence is a variation of A261657, using 4 prime factors instead of 3.
%C Some members of this sequence have properties similar to those in A261656. For example, the sequence of divisors of 3*11*101*12421 = 41399193 is approximately linear on a log scale.
%e 41399193=3*11*101*12421; 101 = ((3^4)+(11^2))/2 and 12421 = ((11^4)+(101^2))/2, so 41399193 is a member.
%p n := 20: L := []: for a from 3 to n do if isprime(a) then for b from a to n^2 do if isprime(b) then c := (a^4+b^2)*(1/2); if isprime(c) then d := (b^4+c^2)*(1/2); if isprime(d) then L := [op(L), a*b*c*d]: end if end if end if end do end if end do; L := sort(L)
%o (PARI) factorsm(n)=my(v=factor(n), f=factor(n)[, 1]~, w=[]); for(i=1, #f, for(j=1, v[i, 2], w=concat(w, f[i]))); w;
%o is(n)=f=factorsm(n);if(#f==4,a=f[1];b=f[2];c=f[3];d=f[4];a<b&&b<c&&c<d&&c==((a^4)+(b^2))/2&&d==((b^4)+(c^2))/2,0) \\ _Anders Hellström_, Aug 28 2015
%Y Cf. A261656, A261657.
%K nonn
%O 1,1
%A _David Ferris_, Aug 28 2015
|
