A030467 Numbers k such that k^2 is a concatenation of two successive numbers.

428, 573, 727, 846, 7810, 36365, 63636, 326734, 673267, 4545454, 5454547, 47058823, 52941178, 331983807, 332667334, 384615386, 422892898, 475524477, 524475524, 577107103, 615384615, 667332667, 668016194, 719964246, 758241758, 804511280, 810873337, 857142859

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base
• nice

Examples

			428^2 = 183184, the concatenation of 183 and 184.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10471 (terms n = 1..53 from Donovan Johnson, terms n = 54..1000 from Giovanni Resta)
• Pante Stanica, Squares as concatenation of consecutive integers, Slides, West Coast Number Theory, Dec 17 2017.

Crossrefs

Cf. A030465, A030466, A054214, A054215, A054216, A020339, A020340.

Programs

Mathematica

t={}; Do[If[EvenQ[y=Length[x=IntegerDigits[n^2]]] && Differences[FromDigits/@Partition[x,y/2]]=={1},AppendTo[t,n]],{n, 5.5*10^6}]; t (* Jayanta Basu, May 25 2013 *)
Sqrt[#]&/@(Select[FromDigits[Flatten[IntegerDigits/@#]]&/@ (Partition[ Range[735*10^6],2,1]),IntegerQ[Sqrt[#]]&]) (* The program takes a long time to run. *) (* Harvey P. Dale, Oct 10 2017 *)

PARI

for(n=1, 10^9, t=eval(concat(Str(n),Str(n+1))); if(issquare(t,&s), print1(s,", "))); /* Antonio Roldán and Joerg Arndt, Dec 31 2012 */

Extensions

a(17) corrected by Donovan Johnson, Jan 03 2013