A065297
a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) properly contained in the digits of a(n+1)^2, with a(0)=1.
Original entry on oeis.org
1, 4, 13, 36, 113, 487, 1036, 3214, 10456, 36786, 100963, 319656, 1001964, 3165969, 10001786, 31626854, 100013919, 316256807, 1000029656, 3162322481, 10000115537
Offset: 0
13^2 = 169 and 36 is the next smallest number whose square (in this case 1296) properly contains the digits 1,6,9.
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import Data.List ((\\), sort)
a065297 n = a065297_list !! n
a065297_list = 1 : f 1 (drop 2 a000290_list) where
f x (q:qs) | null (xs \\ sq) && sort xs /= sort sq = y : f y qs
| otherwise = f x qs
where y = a000196 q; sq = show q; xs = show (x * x)
-- Reinhard Zumkeller, Nov 22 2012
A067971
a(n+1) is the smallest number > a(n) such that the digits of a(n)^3 are all (with multiplicity) properly contained in the digits of a(n+1)^3, with a(0)=1.
Original entry on oeis.org
1, 5, 25, 105, 678, 2685, 6631, 17248, 48056, 109016, 255085, 576468, 1026598, 2161819, 4793623, 10107506, 21624889, 46584891, 100042239, 215671305, 464309988, 1000305876, 2156229901, 4642492109, 10000266599
Offset: 0
5^3 = 125 and 25 is the next smallest number whose cube (in this case 15625) properly contains the digits 1,2,5.
A067973
a(n+1) is the smallest number > a(n) such that the digits of a(n)^3 are all (with multiplicity) contained in the digits of a(n+1)^3, with a(0)=1.
Original entry on oeis.org
1, 5, 8, 25, 105, 678, 2685, 6631, 17248, 48056, 109016, 255085, 576468, 993996, 1026598, 1029697, 1061509, 1089598, 1231339, 1374358, 1753291, 1832389, 1896319, 2161819, 2162446, 2163199, 2231416, 2263201, 2264893, 2674003
Offset: 0
5^3 = 125 and 8 is the next smallest number whose cube (in this case 512) that contains the digits 1,2,5.
A067975
a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) contained in the digits of a(n+1)^2, with a(0)=2.
Original entry on oeis.org
2, 7, 43, 136, 367, 1157, 1822, 3658, 5558, 6196, 9679, 10183, 11794, 17852, 20813, 28354, 32193, 42852, 53787, 55044, 55707, 55983, 57636, 58464, 61719, 70209, 95232, 96354, 96921, 96963, 101407, 114223, 114323, 133564, 162293, 170843
Offset: 0
1157^2 = 1338649 and 1822 is the next smallest number whose square (in this case 3319684) contains the digits 1,3,3,8,6,4,9.
A067714
a(n+1) is the smallest square > a(n) such that the digits of a(n) are all (with multiplicity) properly contained in the digits of a(n+1), with a(0)=4.
Original entry on oeis.org
4, 49, 1849, 18496, 134689, 1338649, 13380964, 103693489, 1036389249, 10283379649, 102743968369, 1003687392964, 10026487930369, 100038463697929, 1000274339968996, 10003462899739969, 100234979989639056
Offset: 0
Showing 1-5 of 5 results.
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