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

Author

M. F. Hasler, Oct 07 2019

Keywords

• nonn
• base
• tabf

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.

Examples

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

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.

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).

Programs

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", ")))