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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A385970 a(n) is the minimum number of powers needed to obtain the n-th term of sequence A385969.

Original entry on oeis.org

1, 2, 1, 2, 2, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 2, 4, 3, 4, 4, 1, 2, 3, 3, 2, 3, 3, 3, 2, 4, 4, 3, 4, 3, 2, 3, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 3, 2, 4, 3, 3, 4, 3, 4, 4, 5, 4, 4, 4, 4, 3, 3, 5, 5, 4, 3, 4, 4, 4, 4, 3, 4, 5, 2, 3, 4, 4, 5, 4, 4, 5, 4, 4, 3, 4, 5, 4, 2, 4, 3, 5, 4, 5
Offset: 1

Views

Author

Alberto Zanoni, Jul 14 2025

Keywords

Comments

The sequence is unbounded (conjectured).

Examples

			a(1) = 1, as  4 = 2^2
a(2) = 2, as 17 = 2^3 + 3^2
a(3) = 1, as 27 = 3^3
a(4) = 2, as 31 = 2^2 + 3^3
a(7) = 3, as 59 = 2^4 + 3^3 + 4^2

Crossrefs

Cf. A385969, A385232, A385233.

A386968 Numbers that can be written in exactly four ways as s_1^x_1 + ... + s_t^x_t, with 1 < s_1 < ... < s_t and {s_1,..., s_t} = {x_1,..., x_t} for some t > 0.

Original entry on oeis.org

331979, 536134, 602342, 848707, 1007017, 1360430, 1484182, 1767157, 1891086, 2024074, 2036922, 2095031, 2097159, 2231826, 2257754, 2292303, 2293830, 2320578, 2440812, 2503676, 2590739, 2744591, 2852016, 2890344, 2914526, 2944901, 2951290, 3019920, 3020295, 3053910, 3121946, 3157114, 3310022
Offset: 1

Views

Author

Alberto Zanoni, Aug 12 2025

Keywords

Examples

			331979 = 2^15 + 4^5  + 5^6 + 6^7 + 7^4 + 15^2
       = 2^2 + 3^8  + 4^9 + 5^3 + 8^4 + 9^5
       = 2^5  + 3^10 + 4^9 + 5^2 + 9^3 + 10^4
       = 2^6 + 3^10 + 4^9 + 5^5 + 6^2 + 9^4 + 10^3.
536134 = 2^6 + 3^12 + 4^3 + 5^5 + 6^4 + 12^2
       = 2^16 + 3^10 + 4^9 + 5^7 + 6^6 + 7^5  + 9^4
       = 2^16 + 4^8  + 5^5 + 6^7 + 7^6 + 8^4  + 16^2
       = 2^18 + 3^11 + 4^4 + 5^7 + 7^5 + 11^3 + 18^2.
602342 = 2^16 + 3^12 + 4^4 + 5^5 + 12^3 + 16^2
       = 2^8  + 3^12 + 4^3 + 5^5 + 6^6 + 8^2 + 12^4
       = 2^13 + 3^8  + 4^2 + 5^3 + 6^7 + 7^5 + 8^6 + 13^4
       = 2^15 + 3^10 + 4^8 + 5^7 + 6^4 + 7^2 + 8^6 + 10^5 + 15^3.
5260225 is not in the sequence as it can be written in exactly five ways a such. - _David A. Corneth_, Aug 16 2025

Links

Crossrefs

Subsequence of A385969.
Cf. A385232, A385233, A385970, A386966, A386967.

A386966 Numbers that can be written in exactly two different ways as s_1^x_1 + ... + s_t^x_t, with 1 < s_1 < ... < s_t and {s_1,..., s_t} = {x_1,..., x_t} for some t > 0.

Original entry on oeis.org

545, 1407, 1492, 2409, 3370, 3605, 3718, 4516, 4523, 4684, 5441, 6348, 7346, 7737, 7865, 7922, 8122, 8538, 9046, 10010, 10037, 10298, 10458, 10554, 10651, 10891, 10953, 11047, 11653, 11853, 11986, 12025, 12449, 13621, 14078, 14098, 14535, 14970, 16138, 16449, 16705, 16905, 17401, 18149, 18161, 18509
Offset: 1

Views

Author

Alberto Zanoni, Aug 12 2025

Keywords

Examples

			 545 = 2^6  + 3^2 + 4^4 + 6^3  = 2^7 + 3^5 + 5^3 + 7^2.
1407 = 2^10 + 3^3 + 4^4 + 10^2 = 2^7 + 3^4 + 4^5 + 5^3 + 7^2.
1492 = 2^10 + 3^5 + 5^3 + 10^2 = 2^7 + 3^6 + 4^4 + 6^2 + 7^3.

Crossrefs

Subsequence of A385969.
Cf. A385232, A385233, A385970, A386967, A386968.

A386967 Numbers that can be written in exactly three different ways as s_1^x_1 + ... + s_t^x_t, with 1 < s_1 < ... < s_t and {s_1,..., s_t} = {x_1,..., x_t} for some t > 0.

Original entry on oeis.org

23506, 23778, 41682, 50261, 53554, 76754, 78289, 92030, 96981, 99913, 101559, 105885, 109094, 114097, 117538, 125943, 132867, 133116, 135697, 143154, 150041, 158539, 160161, 197547, 198333, 204359, 225138, 225530, 265685, 269986, 277243, 280063, 286299, 291016, 295391, 306251, 312341, 313323
Offset: 1

Views

Author

Alberto Zanoni, Aug 12 2025

Keywords

Examples

			23506 = 2^9 + 4^7 + 7^2 + 9^4
      = 2^3 + 3^4 + 4^2 + 5^6 + 6^5
      = 2^4 + 3^8 + 4^5 + 5^6 + 6^3 + 8^2.
23778 = 2^11 + 3^8 + 4^2 + 8^3 + 11^4
      = 2^12 + 3^2 + 4^5 + 5^6 + 6^4 + 12^3
      = 2^10 + 3^8 + 4^6 + 5^3 + 6^5 + 8^4 + 10^2.
41682 = 2^3 + 3^9 + 4^7 + 5^5 + 7^4 + 9^2
      = 2^9 + 3^8 + 4^7 + 5^4 + 7^5 + 8^2 + 9^3
      = 2^14 + 3^8 + 4^6 + 5^2 + 6^5 + 8^4 + 14^3.

Crossrefs

Subsequence of A385969.
Cf. A385232, A385233, A385970, A386966, A386968.

A387099 Numbers that can be written in exactly five ways as s_1^x_1 + ... + s_t^x_t, with 1 < s_1 < ... < s_t and {s_1,..., s_t} = {x_1,..., x_t} for some t > 0.

Original entry on oeis.org

5260225, 7923882, 11054875, 11224211, 11870046, 15466174, 16859617, 16911017, 17276523, 17326946, 18664520, 18668302, 18908170, 19375153, 19706896, 19854394, 20050965, 20757873, 21468249, 24723272, 26689657, 26925803, 26974782, 27214122, 27336893, 28055974
Offset: 1

Views

Author

David A. Corneth, Aug 16 2025

Keywords

Examples

			5260225 = 2^22 + 3^8 + 4^5 + 5^2 + 7^7 + 8^3 + 22^4
        = 2^21 + 3^8 + 4^10 + 7^3 + 8^7 + 10^4 + 21^2
        = 2^7 + 3^14 + 4^5 + 5^8 + 6^6 + 7^3 + 8^2 + 14^4
        = 2^15 + 3^10 + 4^9 + 5^5 + 6^4 + 7^6 + 9^7 + 10^3 + 15^2
        = 2^11 + 3^7 + 4^10 + 5^9 + 6^8 + 7^3 + 8^5 + 9^6 + 10^4 + 11^2.
7923882 = 2^8 + 3^5 + 4^11 + 5^9 + 6^3 + 8^4 + 9^2 + 11^6
        = 2^12 + 3^9 + 4^5 + 5^6 + 6^2 + 7^8 + 8^7 + 9^3 + 12^4
        = 2^14 + 3^13 + 4^4 + 5^5 + 6^7 + 7^8 + 8^6 + 13^2 + 14^3
        = 2^18 + 3^14 + 4^6 + 5^9 + 6^3 + 7^7 + 9^5 + 14^4 + 18^2
        = 2^19 + 3^14 + 4^8 + 5^9 + 6^6 + 8^2 + 9^4 + 14^5 + 19^3.
11054875 = 2^3 + 3^6 + 4^10 + 5^5 + 6^2 + 7^4 + 10^7
         = 2^15 + 3^8 + 4^6 + 5^2 + 6^9 + 7^7 + 8^3 + 9^5 + 15^4
         = 2^22 + 3^12 + 4^2 + 5^6 + 6^7 + 7^8 + 8^5 + 12^3 + 22^4
         = 2^9 + 3^13 + 4^10 + 5^3 + 6^5 + 7^8 + 8^7 + 9^6 + 10^4 + 13^2
         = 2^11 + 3^12 + 4^8 + 5^7 + 6^9 + 7^6 + 8^3 + 9^2 + 11^5 + 12^4.

Links

Crossrefs

Cf. A385969, A386968.

A387100 a(n) is the least number that can be written in exactly n ways as s_1^x_1 + ... + s_t^x_t, with 1 < s_1 < ... < s_t and {s_1,..., s_t} = {x_1,..., x_t}.

Original entry on oeis.org

4, 545, 23506, 331979, 5260225, 10630307
Offset: 1

Views

Author

David A. Corneth, Aug 16 2025

Keywords

Examples

			a(5) = 5260225 via
5260225 = 2^22 + 3^8 + 4^5 + 5^2 + 7^7 + 8^3 + 22^4
        = 2^21 + 3^8 + 4^10 + 7^3 + 8^7 + 10^4 + 21^2
        = 2^7 + 3^14 + 4^5 + 5^8 + 6^6 + 7^3 + 8^2 + 14^4
        = 2^15 + 3^10 + 4^9 + 5^5 + 6^4 + 7^6 + 9^7 + 10^3 + 15^2
        = 2^11 + 3^7 + 4^10 + 5^9 + 6^8 + 7^3 + 8^5 + 9^6 + 10^4 + 11^2,
and no positive integer smaller than 5260225 can be written as such in exactly five ways.

Crossrefs

Cf. A385969, A386968.
Showing 1-6 of 6 results.

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