A328199 Triples (a,b,c) such that (a+b+c)^3 = concat(a,b,c), a, b, c > 0, ordered by size of this value.

5, 1, 2, 9, 11, 25, 418, 1062, 131, 878, 2442, 1125, 938, 2422, 1184, 1212, 1388, 2349, 1287, 1113, 2649, 1623, 2457, 1375, 1713, 2377, 1464, 3689, 1035, 2448, 7890, 10706, 1312, 17147, 18793, 19616, 22072, 11858, 26504, 47051, 15775, 14952

Offset

1,1

Comments

The sequence can be considered as a table with rows of length 3, row(n) = a(3n-2 .. 3n).

A variant of Kaprekar and pseudo-Kaprekar triples, cf. A006887 and A060768.

See A328198 and A328200 (sequence of the values a+b+c and concatenated triples) for more information.

Links

Giovanni Resta, Table of n, a(n) for n = 1..717

Números y algo mas, 9 + 11+ 25 = 91125^(1/3) etc, post on facebook.com, Sep 30 2019.

Example

5+1+2 = 512^(1/3) = 8,
9+11+25 = 91125^(1/3) = 45,
418+1062+131 = (4181062131)^(1/3) = 1611, ...

Prog

(PARI) is(n, Ln=A055642(n), n3=n^3, Ln3=A055642(n3))={my(ab, c); for(Lc=Ln3-2*Ln, Ln, [ab, c]=divrem(n3, 10^Lc); n-c<10^(Ln-1) || c < 10^(Lc-1) || for( Lb=Ln3-Ln-Lc, Ln, vecsum(divrem(ab, 10^Lb)) == n-c && ab%10^Lb>=10^(Lb-1)&& return(concat(divrem(ab, 10^Lb)~, c))))} \\ A055642(n)=logint(n, 10)+1 = #digits(n)
for( Ln=1, oo, for( n=10^(Ln-1), 10^Ln-1, (t=is(n, Ln))&& print1(t", ")))

Crossrefs

Cf. A328198 (row sums), A328200 (rows concatenated), A006887 & A291461 (Kaprekar numbers), A060768 (pseudo Kaprekar numbers); A000578 (the cubes), A055642 (number of digits of n).

Sequence in context: A021665 A226613 A274989 * A289690 A088781 A085608

Adjacent sequences: A328196 A328197 A328198 * A328200 A328201 A328202

Keyword

nonn,base,tabf

Author

M. F. Hasler, Oct 07 2019

Status

approved