A048422 Numbers k such that k^2 is formed from two subsquares that overlap in a single digit.

57, 285, 475, 604, 1442, 2225, 6293, 6645, 9175, 9607, 10815, 16349, 18493, 25375, 34825, 38025, 41225, 48035, 54075, 54758, 56605, 60125, 92971, 98075, 104956, 106885, 162225, 196096, 264904, 392125, 534425, 572375, 597675, 635625, 684475

Offset

1,1

Comments

Subsquares with leading and/or trailing zeros not included. Subsquares are at least 2 digits long.

Links

Table of n, a(n) for n=1..35.

Example

57 is a term because 57^2 = 3249 in which we see 324 = 18^2 and 49 = 7^2 overlapping in a single digit, namely the digit 4.
162225 is a term:
162225^2 = 26316950625
   513^2 = 263169
   975^2 =      950625
                ^
                |
         1-digit overlap

Mathematica

qQ[w_] := w[[1]] > 0 && w[[-1]] > 0 && IntegerQ@ Sqrt@ FromDigits[w]; ok[n_] := n>9 && Mod[n, 10] > 0 && Block[{d = IntegerDigits[ n^2], m}, m = Length[d]; AnyTrue[ Range[2, m-1], qQ[ Take[d, #]] && qQ[Take[d, {#, m}]] &]]; Select[Range[10^5], ok] (* Giovanni Resta, Oct 14 2019 *)

Crossrefs

Cf. A000290, A048421.

Sequence in context: A158668 A145296 A176635 * A157651 A251263 A367277

Adjacent sequences: A048419 A048420 A048421 * A048423 A048424 A048425

Keyword

nonn,base

Author

Patrick De Geest, Apr 15 1999

Status

approved