A261658 Numbers with 4 prime factors a < b < c < d such that 2c = a^4 + b^2 and 2d = b^4 + c^2.

41399193, 195157536843, 548699719043, 3036956318943, 320218213825307, 4132518238158443, 4519695415117057, 6270713759856601, 18507175540175893, 29390150965410193, 106799085933816293, 183320084770933043, 220070939141434093, 481373412121678901

Offset

1,1

Comments

This sequence is a variation of A261657, using 4 prime factors instead of 3.

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.

Links

Table of n, a(n) for n=1..14.

Example

41399193=3*11*101*12421; 101 = ((3^4)+(11^2))/2 and 12421 = ((11^4)+(101^2))/2, so 41399193 is a member.

Maple

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)

Prog

(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;
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

Crossrefs

Cf. A261656, A261657.

Sequence in context: A178204 A334583 A130681 * A274812 A251306 A198168

Adjacent sequences: A261655 A261656 A261657 * A261659 A261660 A261661

Keyword

nonn

Author

David Ferris, Aug 28 2015

Status

approved