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A179856 Numbers n such that n^3 can be obtained from n by inserting internal (but not necessarily contiguous) digits. 1
10, 11, 29, 34, 99, 100, 101, 106, 109, 110, 114, 119, 120, 124, 125, 274, 275, 276, 279, 281, 290, 296, 299, 314, 315, 316, 319, 320, 324, 325, 329, 330, 335, 336, 340, 966, 970, 975, 976, 979, 986, 990, 996, 999, 1000, 1001, 1004, 1005, 1006, 1010, 1020, 1021, 1024, 1025, 1034, 1049, 1051 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is to A046851 as cubes A000578 are to squares A000290. A subset of A086458 (but note that, i.e., 104^3 = 1124864 starts and ends with the same digits as 104, but lacks an internal "0"). If we require the inserted digits to fill contiguous places, another sequence results, which does not contain 106, for example.

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

34^3 = 39304 (insert "930" into "34").

106^3 = 1191016 (insert "191" and "1" into "106").

MAPLE

A000030 := proc(n) if n= 0 then 0; else op(-1, convert(n, base, 10)) ; end if; end proc:

A010879 := proc(n) n mod 10 ; end proc:

isA086458 := proc(n) A000030(n) = A000030(n^3) and A010879(n) = A010879(n^3) ; end proc:

subsI := proc(c, L) for i from 1 to nops(L) do if op(i, L) = c then return i; end if; end do; return -1 ; end proc:

isSubS := proc(Sub, Sup) if nops(Sub) = 1 then if subsI(op(1, Sub), Sup) > 0 then return true; else return false; end if; elif nops(Sub) = 0 then return true; else f := subsI(op(1, Sub), Sup) ; if f < 0 then return false; else procname( subsop(1=NULL, Sub), [op(f+1..nops(Sup), Sup)] ) ; end if; end if; end proc:

isA179856 := proc(n) if isA086458(n) then dgsn := convert(n, base, 10) ; dgsn := op(2..nops(dgsn)-1, dgsn) ; dgsn3 := convert(n^3, base, 10) ; dgsn3 := op(2..nops(dgsn3)-1, dgsn3) ; isSubS([dgsn], [dgsn3]) ; else false; end if; end proc:

for n from 10 to 1400 do if isA179856(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Jan 30 2011

CROSSREFS

Cf. A000578, A046851, A086458.

Sequence in context: A056067 A300678 A086458 * A098795 A108580 A041208

Adjacent sequences:  A179853 A179854 A179855 * A179857 A179858 A179859

KEYWORD

nonn,base,easy

AUTHOR

Jonathan Vos Post, Jan 28 2011

STATUS

approved

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Last modified July 17 02:10 EDT 2019. Contains 325092 sequences. (Running on oeis4.)