A048383 Numbers k such that replacing each nonzero digit d with the d-th prime (replacing each 0 digit with a 1) yields a square.

0, 13, 113, 2410, 4113, 6113, 8210, 14113, 23410, 28113, 33113, 34010, 35113, 51113, 62113, 71113, 76610, 81410, 93113, 101310, 117010, 123113, 242210, 253113, 279710, 298113, 300113, 351010, 513410, 529113, 544113, 616113, 634113

Offset: 1

Author

Patrick De Geest, Mar 15 1999

Keywords

• nonn
• base

Examples

			28113 = (2)(8)(1)(1)(3) -> (3)(19)(2)(2)(5) = 319225 = 565^2.
		

Crossrefs

Cf. A000290, A048380, A048384.

Programs

Mathematica

Select[Range[0,650000],IntegerQ[Sqrt[FromDigits[Flatten[IntegerDigits/@ (If[#==0,1,Prime[#]]&/@IntegerDigits[#])]]]]&]  (* Harvey P. Dale, Mar 27 2011 *)

Extensions

Definition edited and offset corrected by M. F. Hasler, Oct 11 2019