cp's OEIS Frontend

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 1-4 of 4 results.

A385969 Numbers that can be written 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

4, 17, 27, 31, 32, 57, 59, 84, 89, 100, 105, 127, 145, 149, 166, 177, 202, 204, 245, 254, 256, 260, 273, 276, 283, 287, 289, 313, 320, 322, 340, 347, 348, 356, 368, 372, 377, 383, 400, 422, 433, 460, 465, 468, 480, 532, 545, 548, 568, 576, 593, 603, 620, 624, 628, 673, 688, 700
Offset: 1

Views

Author

Alberto Zanoni, Jul 13 2025

Keywords

Comments

The value 1 is excluded because for t = 2 one would obtain 1^x_1 + x_1^1 = 1 + x_1, which for x_1 = 2,3,4,... would give the trivial sequence 3,4,5,6,...

Examples

			a(1) =  4 : 2^2 = 4 (t = 1)
a(2) = 17 : 2^3 + 3^2 = 8 + 9 = 17 (t = 2)
a(3) = 27 : 3^3 = 27 (t = 1)
a(4) = 31 : 2^2 + 3^3 = 4 + 27 = 31 (t = 2)

Links

Crossrefs

Cf. A385232, A385233, A385970.

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.
Showing 1-4 of 4 results.

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