A062118 -id:A062118 - cp's OEIS frontend

A046829 Numbers k such that digits of k^2 include digits of k as subsequence.

0, 1, 5, 6, 10, 11, 25, 50, 60, 76, 95, 96, 100, 101, 105, 110, 125, 205, 250, 305, 371, 376, 405, 441, 500, 501, 505, 506, 525, 600, 601, 605, 625, 676, 705, 756, 760, 805, 825, 826, 905, 946, 950, 960, 976, 995, 996, 1000, 1001, 1005, 1006, 1010, 1011

Offset: 1

David W. Wilson

Cf. A046827, A062118 (subsequence).

fQ[n_]:=LongestCommonSequence[ToString[n^2],ToString[n]]==ToString[n];
Select[Range[0,1011],fQ[#]&] (* Ivan N. Ianakiev, Dec 29 2023 *)

from itertools import count, islice
def A046829_gen(startvalue=0): # generator of terms >= startvalue
    for k in count(max(startvalue,0)):
        c = iter(str(k**2))
        if all(map(lambda b:any(map(lambda a:a==b,c)),str(k))):
            yield k
A046829_list = list(islice(A046829_gen(),20)) # Chai Wah Wu, Apr 03 2023

Offset 1 from Alois P. Heinz, Apr 03 2023

A062120 Numbers k such that k has sqrt(k) as its middle digits.

Original entry on oeis.org

1, 2500, 3600, 62500, 14379264, 57760000, 141376000000, 245495475625, 390625000000, 943971582724, 4482669527413081, 8790937600000000, 31561776563446336, 10235319926865509025

Offset: 1

Brian Wallace (wallacebrianedward(AT)yahoo.co.uk), Jun 28 2001

Cf. A062118.

Do[ If[ StringPosition[ ToString[n^2], ToString[n]] [[1, 1]] == (Ceiling[ Log[10, n^2] ] - Ceiling[ Log[10, n] ])/2 + 1, Print[n^2] ], {n, 1, 10^9} ]

a(n) = A062118(n)^2.

A225795 Smallest k > 1 such that k^n has k as its middle digits, or 0 if no such k exists.

Original entry on oeis.org

2, 50, 50, 60, 70, 6, 2, 7600, 47, 5, 4, 93, 6, 34, 5, 9600, 71, 4, 74, 320, 3, 372, 13, 846, 32, 9600, 339, 9765, 202, 3, 69, 6, 9900, 13, 8586, 9600, 4, 46, 3, 4, 446, 3, 9900, 4, 1256, 614, 819, 3365, 8, 36400, 76, 647, 35, 39548, 9900, 4740

Offset: 1

Michel Lagneau, Jul 27 2013

Is a(88) the first 0? If a(88) is nonzero, it is greater than 2 * 10^8. - T. D. Noe, Jul 29 2013

			a(6) = 6 because 6^6 = 46656 has 6 as its middle digit.

Cf. A062118.

Table[k = 2; While[c0 = IntegerDigits[k]; c1 = IntegerDigits[k^n]; len0 = Length[c0]; len1 = Length[c1];  f = (len1 - len0)/2; ! (OddQ[len0] == OddQ[len1] && c0 == Take[c1, {f + 1, f + len0}]), k++]; k, {n, 56}] (* T. D. Noe, Jul 29 2013 *)

Corrected by T. D. Noe, Jul 29 2013

A227548 Numbers n such that n^3 has n as its middle digits.

Original entry on oeis.org

1, 50, 56, 60, 90, 4900, 5100, 7500, 7600, 9900, 12500, 499000, 501000, 624000, 625000, 749000, 751000, 875000, 999000, 1249000, 13427757, 49990000, 50010000, 56250000, 62490000

Offset: 1

Vincenzo Librandi, Jul 30 2013

			a(6)=4900 because 4900^3 = 117649000000 has 4900 as its middle digits.

Cf. A062118.

Do[If[StringPosition[ToString[n^3], ToString[n]][[1, 1]] == (Ceiling[Log[10, n^3]] - Ceiling[Log[10, n]]) / 2 + 1, Print[n]], {n, 0, 10^8}]

cp's OEIS Frontend

A046829 Numbers k such that digits of k^2 include digits of k as subsequence.

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A062120 Numbers k such that k has sqrt(k) as its middle digits.

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A225795 Smallest k > 1 such that k^n has k as its middle digits, or 0 if no such k exists.

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A227548 Numbers n such that n^3 has n as its middle digits.

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