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A048422 Numbers k such that k^2 is formed from two subsquares that overlap in a single digit. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A043399

Adjacent sequences:  A048419 A048420 A048421 * A048423 A048424 A048425

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Apr 15 1999

STATUS

approved

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Last modified July 2 09:32 EDT 2022. Contains 354999 sequences. (Running on oeis4.)