A275343 Numbers with at least three digits and with the property that the sum of the cubes of the first and last digit equals the number obtained when the first and last digits are deleted.

110, 121, 192, 280, 291, 1010, 1021, 1092, 1283, 1654, 2080, 2091, 2162, 2353, 2724, 3270, 3281, 3352, 3543, 3914, 4640, 4651, 4722, 4913, 10010, 10021, 10092, 10283, 10654, 11265, 12176, 13447, 15138, 17309, 20080, 20091, 20162, 20353, 20724, 21335, 22246, 23517, 25208, 27379, 30270, 30281, 30352

Offset

1,1

Comments

More precisely, numbers n = d_1 d_2 d_3 ... d_k such that (d_1)^3 + (d_k)^3 = d_2 d_3 ... d_{k-1}.

Here, d_2 may or may not be zero.

This sequence is infinite (it contains the numbers 1000...00010).

A274945 is a similar sequence where squares are used instead of cubes.

Links

Table of n, a(n) for n=1..47.

Biswarup Banerjee, The StairCase Sequence, Para: 8

Example

12176 is a term because 1^3 + 6^3 = 217, coming from 1_217_6;
607288 is a term because 6^3 + 8^3 = 728, coming from 6_0728_8.

Mathematica

Select[Range[10^2, 10^5], (#[[1]]^3 + #[[-1]]^3) == FromDigits@ Most@ Rest@ # &@ IntegerDigits@ # &] (* Michael De Vlieger, Jul 25 2016 *)

Prog

(PARI) isok(n) = my(d = digits(n)); d[1]^3+d[#d]^3 == (n - d[#d] - 10^(#d-1)*d[1])/10; \\ Michel Marcus, Sep 24 2016

Crossrefs

Cf. A274945, A274944.

Sequence in context: A101317 A274945 A274944 * A059469 A114068 A073494

Adjacent sequences: A275340 A275341 A275342 * A275344 A275345 A275346

Keyword

nonn,base

Author

Biswarup Banerjee, Jul 23 2016

Status

approved