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A030467
Numbers k such that k^2 is a concatenation of two successive numbers.
23
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
1,1
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.
EXAMPLE
428^2 = 183184, the concatenation of 183 and 184.
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 *)
PROG
(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 */
KEYWORD
nonn,base,nice
EXTENSIONS
a(17) corrected by Donovan Johnson, Jan 03 2013
STATUS
approved