A018143 -id:A018143 - cp's OEIS frontend

A374025 a(n) is the largest digit sum of all n-digit fifth powers.

1, 5, 9, 27, 27, 36, 45, 46, 52, 63, 72, 80, 89, 90, 99, 104, 108, 119, 126, 143, 137, 152, 157, 162, 175, 180, 182, 189, 198, 208, 209, 216, 225, 234, 236, 250, 253, 270, 270, 284, 286, 288, 297, 310, 315, 323, 324, 334, 341, 346, 351, 364

Offset: 1

Zhining Yang, Jun 25 2024

			a(5) = 27 because 27 is the largest digital sum encountered among all 5-digit fifth powers (16807, 32768, 59049).

Cf. A055566, A018141, A018143, A348300, A373727, A373914.

Table[Max@Map[Total@IntegerDigits[#^5] &, Range[Ceiling[10^((n - 1)/5)], Floor[(10^n-1)^(1/5)]]], {n, 40}]

from sympy import integer_nthroot
def A374025(n): return max(sum(int(d) for d in str(m**5)) for m in range((lambda x:x[0]+(x[1]^1))(integer_nthroot(10**(n-1),5)),1+integer_nthroot(10**n-1,5)[0])) # Chai Wah Wu, Jun 26 2024

a(41)-a(49) from Chai Wah Wu, Jun 26 2024

a(50)-a(52) from Chai Wah Wu, Jun 27 2024

A130080 Smallest number whose sixth power has n digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 10, 15, 22, 32, 47, 69, 100, 147, 216, 317, 465, 682, 1000, 1468, 2155, 3163, 4642, 6813, 10000, 14678, 21545, 31623, 46416, 68130, 100000, 146780, 215444, 316228, 464159, 681293, 1000000, 1467800, 2154435, 3162278, 4641589

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of sixth root of 10 rounded up.

			6^6 = 46656 has five digits, 7^6 = 117649 has six digits, hence a(6) = 7.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130081 to A130084 (smallest number whose seventh ... tenth power has n digits).

[ Ceiling(Root(10^(n-1),6)): n in [1..41] ];

Table[(Ceiling[10^((n - 1)/6)]), {n, 1, 100}] (* Vincenzo Librandi, Sep 20 2013 *)

from sympy import integer_nthroot
def A130080(n):
    a, b = integer_nthroot(10**(n-1),6)
    return a+(not b) # Chai Wah Wu, Jun 19 2024

a(n) = ceiling(10^((n-1)/6)).

A130084 Smallest number whose tenth power has at least n digits.

Original entry on oeis.org

1, 2, 2, 2, 3, 4, 4, 6, 7, 8, 10, 13, 16, 20, 26, 32, 40, 51, 64, 80, 100, 126, 159, 200, 252, 317, 399, 502, 631, 795, 1000, 1259, 1585, 1996, 2512, 3163, 3982, 5012, 6310, 7944, 10000, 12590, 15849, 19953, 25119, 31623, 39811, 50119, 63096, 79433, 100000

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of tenth root of 10 rounded up.

			3^10 = 59049 has five digits, 4^10 = 1048576 has seven digits, hence a(6) = a(7) = 4.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011279, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130083 (smallest number whose sixth ... ninth power has n digits).

[Ceiling(Root(10^(n-1),10)): n in [1..51]];

Table[(Ceiling[10^((n - 1)/10)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 20 2013 *)

from sympy import integer_nthroot
def A130084(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),10)) # Chai Wah Wu, Jun 20 2024

a(n) = ceiling(10^((n-1)/10)).

A018141 Powers of fifth root of 10 rounded down.

Original entry on oeis.org

1, 1, 2, 3, 6, 10, 15, 25, 39, 63, 100, 158, 251, 398, 630, 1000, 1584, 2511, 3981, 6309, 10000, 15848, 25118, 39810, 63095, 100000, 158489, 251188, 398107, 630957, 1000000, 1584893, 2511886, 3981071, 6309573

Offset: 0

N. J. A. Sloane

nonn

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A018142, A018143.

Floor[(10^(1/5))^Range[0,40]] (* Harvey P. Dale, Sep 24 2012 *)

a(n) = sqrtnint(10^n, 5); \\ Michel Marcus, Jun 26 2024

A130083 Smallest number whose ninth power has at least n digits.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 6, 8, 10, 13, 17, 22, 28, 36, 47, 60, 78, 100, 130, 167, 216, 279, 360, 465, 600, 775, 1000, 1292, 1669, 2155, 2783, 3594, 4642, 5995, 7743, 10000, 12916, 16682, 21545, 27826, 35939, 46416, 59949, 77427, 100000, 129155, 166811, 215444

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of ninth root of 10 rounded up.

			2^9 = 512 has three digits, 3^9 = 19683 has five digits, hence a(4) = a(5) = 3.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011278, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130084 (smallest number whose sixth ... tenth power has n digits).

[ Ceiling(Root(10^(n-1),9)): n in [1..49] ];

Table[(Ceiling[10^((n - 1)/9)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 21 2013 *)

from sympy import integer_nthroot
def A130083(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),9)) # Chai Wah Wu, Jun 20 2024

a(n) = ceiling(10^((n-1)/9)).

A130081 Smallest number whose seventh power has at least n digits.

Original entry on oeis.org

1, 2, 2, 3, 4, 6, 8, 10, 14, 20, 27, 38, 52, 72, 100, 139, 194, 269, 373, 518, 720, 1000, 1390, 1931, 2683, 3728, 5180, 7197, 10000, 13895, 19307, 26827, 37276, 51795, 71969, 100000, 138950, 193070, 268270, 372760, 517948, 719686, 1000000, 1389496

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of seventh root of 10 rounded up.

			1^7 = 1 has 1 digit, 2^7 = 128 has three digits, hence a(2) = a(3) = 2.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011276, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130084 (smallest number whose sixth ... tenth power has n digits).

[Ceiling(Root(10^(n-1),7)): n in [1..44]];

Table[(Ceiling[10^((n - 1)/7)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 20 2013 *)

from sympy import integer_nthroot
def A130081(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),7)) # Chai Wah Wu, Jun 20 2024

a(n) = ceiling(10^((n-1)/7)).

A130082 Smallest number whose eighth power has at least n digits.

Original entry on oeis.org

1, 2, 2, 3, 4, 5, 6, 8, 10, 14, 18, 24, 32, 43, 57, 75, 100, 134, 178, 238, 317, 422, 563, 750, 1000, 1334, 1779, 2372, 3163, 4217, 5624, 7499, 10000, 13336, 17783, 23714, 31623, 42170, 56235, 74990, 100000, 133353, 177828, 237138, 316228, 421697

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of eighth root of 10 rounded up.

			9^8 = 43046721 has eight digits, 10^8 = 100000000 has nine digits, hence a(9) = 10.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011277, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130084 (smallest number whose sixth ... tenth power has n digits).

[ Ceiling(Root(10^(n-1),8)): n in [1..46] ];

Table[(Ceiling[10^((n - 1)/8)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 20 2013 *)

from sympy import integer_nthroot
def A130082(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),8)) # Chai Wah Wu, Jun 20 2024

a(n) = ceiling(10^((n-1)/8)).

cp's OEIS Frontend

A374025 a(n) is the largest digit sum of all n-digit fifth powers.

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A130080 Smallest number whose sixth power has n digits.

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A130084 Smallest number whose tenth power has at least n digits.

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A018141 Powers of fifth root of 10 rounded down.

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A130083 Smallest number whose ninth power has at least n digits.

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A130081 Smallest number whose seventh power has at least n digits.

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A130082 Smallest number whose eighth power has at least n digits.

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