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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.
0
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.
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
Sequence in context: A101317 A274945 A274944 * A059469 A114068 A073494
KEYWORD
nonn,base
AUTHOR
Biswarup Banerjee, Jul 23 2016
STATUS
approved