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 A363905 Numbers whose square and cube taken together contain each decimal digit. 4
 69, 128, 203, 302, 327, 366, 398, 467, 542, 591, 593, 598, 633, 643, 669, 690, 747, 759, 903, 923, 943, 1016, 1018, 1027, 1028, 1043, 1086, 1112, 1182, 1194, 1199, 1233, 1278, 1280, 1282, 1328, 1336, 1364, 1396, 1419, 1459, 1463, 1467, 1472, 1475 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The first term, a(1) = 69, is the only number for which the square and the cube together contain each decimal digit 0 to 9 exactly once. a(820) = 6534 is the only number of which the square and cube taken together contain each digit 0 to 9 exactly twice. LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10000 Harold Suarez, Interesting..., Number Theory group on LinkedIn, June 2023. EXAMPLE 69^2 = 4761, 69^3 = 328509, which together contain each digit 0-9 exactly once. MATHEMATICA fQ[n_] := Union[ Join[ IntegerDigits[n^2], IntegerDigits[n^3]]] == {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; Select[Range@1500, fQ] (* Robert G. Wilson v, Jun 27 2023 *) PROG (PARI) is(k)=#setunion(Set(digits(k^2)), Set(digits(k^3)))>9 select(is, [1..9999]) (Python) from itertools import count, islice def A363905_gen(startvalue=1): # generator of terms >= startvalue return filter(lambda n:len(set(str(n**2))|set(str(n**3)))==10, count(max(startvalue, 1))) A363905_list = list(islice(A363905_gen(), 20)) # Chai Wah Wu, Jun 27 2023 CROSSREFS Cf. A036744, A054038, A071519 and A156977 for "pandigital" squares. Cf. A119735: Numbers n such that every digit occurs at least once in n^3. Sequence in context: A004237 A004238 A039541 * A044192 A044573 A063355 Adjacent sequences: A363902 A363903 A363904 * A363906 A363907 A363908 KEYWORD nonn,base,less AUTHOR M. F. Hasler, Jun 27 2023 STATUS approved

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Last modified December 6 21:43 EST 2023. Contains 367616 sequences. (Running on oeis4.)