A387302 Numbers k that can be written as k = 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 such that for all possible representations of k the permutations connecting (s_1,...,s_t) with (x_1,...,x_t) are cyclic.

4, 17, 27, 32, 57, 89, 100, 105, 145, 166, 177, 254, 256, 276, 289, 320, 348, 368, 377, 480, 548, 568, 593, 673, 730, 739, 773, 777, 845, 865, 892, 922, 932, 945, 1036, 1065, 1124, 1138, 1164, 1174, 1230, 1236, 1250, 1338, 1355, 1376, 1410, 1433, 1486, 1509, 1533, 1601, 1649, 1652, 1692, 1898, 1930, 2006, 2033, 2049, 2089

Offset

1,1

Comments

Every number in A385969 can be written as a (possibly trivial) sum of numbers in this sequence.

Links

Table of n, a(n) for n=1..61.

Alberto Zanoni, BE-numbers

A. Zanoni and M. Zanoni, Sums of bases-exponents positive integer powers, Analele ştiinţifice ale Universităţii "Ovidius" Constanţa, 34-2 (2026), 197-210.

Example

See examples in A385969 (note that 31 is excluded as 31 = 2^2 + 3^3).
32 = 2^4 + 4^2.
57 = 2^5 + 5^2.
89 = 2^4 + 3^2 + 4^3.
545 does not appear: the permutations associated with both representations 2^6 + 3^2 + 4^4 + 6^3 and 2^7 + 3^5 + 5^3 + 7^2 are not cyclic.
2409 does not appear: the permutation related to 2^6 + 4^5 + 5^2 + 6^4 is cyclic but the one related to 2^8 + 3^6 + 4^3 + 6^4 + 8^2 is not.
4684 appears: the permutations associated with both representations 2^7 + 3^4 + 4^6 + 6^2 + 7^3 and 2^8 + 3^5 + 4^3 + 5^2 + 8^4 are cyclic.

Crossrefs

Subsequence of A385969.

Cf. A385232, A385233, A385970, A386966, A386967, A386968, A387099, A387100.

Sequence in context: A061387 A366210 A385969 * A335593 A319970 A272834

Adjacent sequences: A387299 A387300 A387301 * A387303 A387304 A387305

Keyword

nonn,changed

Author

Alberto Zanoni, Aug 25 2025

Status

approved