A073173 Square composite numbers with square subscripts.

4, 9, 16, 1225, 6036849, 10909809, 29484900, 326561041, 653058025, 952833424, 10487398464

Offset

1,1

Comments

a(12) > 5*10^11. - Donovan Johnson, Feb 06 2010

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

a(n) = A002808(A073172(n)). - Amiram Eldar, Oct 11 2024

Example

a(4) = 1225 = 35^2 = c(1024) = c(32^2).

Mathematica

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

Prog

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

Crossrefs

Cf. A002808, A073171, A073172.

Sequence in context: A082920 A204434 A110979 * A313352 A253601 A313353

Adjacent sequences: A073170 A073171 A073172 * A073174 A073175 A073176

Keyword

nonn,more

Author

Labos Elemer, Jul 19 2002

Extensions

a(10)-a(11) from Donovan Johnson, Feb 06 2010

Status

approved