A038692 Square numbers that are concatenations of two or more prime numbers.

25, 225, 289, 361, 529, 729, 2401, 2601, 2809, 4761, 5329, 5929, 7225, 7569, 11449, 11881, 13225, 15129, 19881, 21609, 22801, 23409, 24649, 25281, 26569, 27225, 29241, 29929, 31329, 32761, 34969, 36481, 39601, 47961, 52441, 53361, 54289, 55225, 57121, 58081

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A166503 (the square roots).

Programs

Mathematica

ric[d_] := PrimeQ@ FromDigits@ d || AnyTrue[ TakeDrop[d, #] & /@ Range[ Length[d] - 1], #[[2,1]] > 0 && PrimeQ@ FromDigits@ #[[1]] && ric@ #[[2]] &]; ok[n_] := If[ EvenQ[n] && Mod[n, 10] != 2, False, ric@ IntegerDigits@ n]; Select[ Range[300]^2, ok] (* Giovanni Resta, Mar 16 2020 *)

PARI

forstep(n=1, 300, 2, is_A152242(n^2) & print1(n^2, ", ")) \\ M. F. Hasler, Mar 19 2012

Formula

A038692(n) = A166503(n)^2. As a set, A038692 = A000290 intersection A152242 = A016754 intersection A152242. - M. F. Hasler, Mar 19 2012

Extensions

Edited by N. J. A. Sloane, Oct 18 2009, incorporating corrections from M. F. Hasler and Zak Seidov.