A073172 The value of index for composite numbers with square subscripts which are also square numbers.

1, 4, 9, 1024, 5621641, 10188864, 27657081, 308950929, 619113924, 904265041, 10011203136

Offset

1,2

Comments

a(12) > 10^12, if it exists. - Amiram Eldar, Oct 11 2024

Links

Table of n, a(n) for n=1..11.

Formula

Solutions to c(x^2) = y^2, values of x^2; where c(j) is the j-th composite number; see program.

A002808(a(n)) = A073173(n). - Amiram Eldar, Oct 11 2024

Example

a(4) = 1024 = 32^2 corresponds to the composite number 1225 = 35^2.

Mathematica

c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x]; Do[s=c[n^2]; If[IntegerQ[Sqrt[s]], Print[n^2]], {n, 1, 1000000}]

Prog

(PARI) lista(cmax) = {my(k = 0); forcomposite(c = 1, , k++; if(issquare(k) && issquare(c), print1(k, ", "))); } \\ Amiram Eldar, Oct 11 2024

Crossrefs

Cf. A002808, A073171, A073173.

Sequence in context: A254959 A028869 A179935 * A168139 A258660 A260305

Adjacent sequences: A073169 A073170 A073171 * A073173 A073174 A073175

Keyword

nonn,more

Author

Labos Elemer, Jul 19 2002

Extensions

a(9)-a(11) from Donovan Johnson, Jan 24 2011

Status

approved