A294661 Numbers whose square contains all of the digits 1 through 9.

11826, 12363, 12543, 14676, 15681, 15963, 18072, 19023, 19377, 19569, 19629, 20316, 22887, 23019, 23178, 23439, 24237, 24276, 24441, 24807, 25059, 25572, 25941, 26409, 26733, 27129, 27273, 29034, 29106, 30384, 32043, 32286, 33144, 34273, 35172, 35337, 35713, 35756, 35757, 35772, 35846, 35853

Offset

1,1

Comments

The sequence has asymptotic density 1: it contains "almost all" numbers.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

11826^2 = 139854276 contains all digits from 1 to 9 exactly once.
The same is true for all terms up to 30384 whose square is 923187456. These terms are also listed in A071519, they form a subsequence of A054037.
The next 3 terms, 32043 (32043^2 = 1026753849), 32286 (32286^2 = 1042385796) and 33144 (33144^2 = 1098524736) contain all of the digits '0' through '9' exactly once: They are the first terms of A054038.
The next term, 34273 with 34273^2 = 1174638529, does not have this property, but the next two are again of that type (35172^2 = 1237069584 and 35337^2 = 1248703569).

Mathematica

Select[Range[#, # + 3*10^4] &@ 11111, AllTrue[Most@ DigitCount[#^2], # > 0 &] &] (* Michael De Vlieger, Nov 08 2017 *)

Prog

(PARI) is_A294661(n)=#select(t->t, Set(digits(n^2)))>8
N=100; for(k=10^4, oo, is_A294661(k)||next; print1(k", "); N--||break)

Crossrefs

Cf. A054037, A071519 (finite subsequence of the first 30 terms), A054038.

Sequence in context: A223296 A110846 A071519 * A347144 A188310 A185496

Adjacent sequences: A294658 A294659 A294660 * A294662 A294663 A294664

Keyword

nonn,base

Author

M. F. Hasler, Nov 08 2017

Status

approved