A374268 Numbers whose squares have a unique pattern of identical digits among the squares.
38, 88, 122, 141, 173, 194, 201, 212, 216, 236, 258, 264, 342, 365, 369, 380, 408, 437, 450, 469, 474, 475, 511, 526, 527, 548, 583, 638, 662, 688, 715, 725, 738, 744, 745, 746, 765, 796, 804, 813, 816, 836, 880, 893, 898, 908, 970, 995, 1020
Offset: 1
Examples
The first term of this sequence is 38, because the first cryptarithmically unique square is 38^2=1444. This means that no other square shares the same pattern "ABBB" of repeating digits. Counterexample: 12 is not in this sequence because 12^2=144 has the same pattern "ABB" of repeating digits as 400=20^2. Equivalently, A358497(144)=A358497(400)=122. The alphametic puzzle SEA^2 = BIKINI has a solution 437^2 = 190969 (K=0, B=1, E=3, S=4, N=6, A=7, I=9). This solution is unique because 437 is a term in this sequence.
Links
- Wikipedia, Verbal arithmetic.
Crossrefs
Cf. A374267 (cryptarithmically unique squares).
Programs
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Mathematica
NumOfDigits = 4; (*Maximal integer length to be searched for*) A358497[k_] := With[{pI = Values@PositionIndex@IntegerDigits@k}, MapIndexed[#1 -> Mod[#2[[1]], 10] &, pI, {2}] // Flatten // SparseArray // FromDigits]; Extract[Extract[Select[Tally[Table[{i, A358497[i^2]}, {i, 1, 10^NumOfDigits - 1}], #1[[2]] == #2[[2]] &], #[[2]] == 1 &], {All, 1}], {All, 1}]
Formula
a(n) = sqrt(A374267(n)).
Comments