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A299792 Numbers k such that A177894(k) = 0. 2
0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1001, 1010, 1012, 1023, 1034, 1045, 1056, 1067, 1078, 1089, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 1210, 1212, 1221, 1232, 1243, 1254, 1265, 1276, 1287, 1298, 1313 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A one-digit number a is in this sequence if and only if a = 0.

A two-digit number ab is in this sequence if and only if a = b.

A three-digit number abc is in this sequence if and only if a = b = c.

A four-digit number abcd is in this sequence if and only if a + c = b + d or (a = c and b = d)

A239019 is trivially a subsequence (because the corresponding circular matrices each contains at least two identical rows or columns). {a(n)} \ A239019 is given as A317291.

LINKS

Table of n, a(n) for n=1..50.

Eric Weisstein's World of Mathematics, Circulant Matrix

Wikipedia, Circulant matrix

EXAMPLE

1452 is a term because the value of the following determinant is 0:

| 1 4 5 2 |

| 4 5 2 1 |

| 5 2 1 4 |

| 2 1 4 5 |

MAPLE

with(linalg): P:=proc(n) local a, b, c, d, j, k, t: d:=ilog10(n)+1:

a:=convert(n, base, 10): c:=[]: for k from 1 to nops(a) do

c:=[op(c), a[-k]]: od: t:=[op([]), c]: for k from 2 to d do

b:=[op([]), c[nops(c)]]: for j from 1 to nops(c)-1 do b:=[op(b), c[j]]: od;

c:=b: t:=[op(t), c]: od: if 0=det(t) then n; fi: end: 0, seq(P(i), i=1..1313); # Paolo P. Lava, Feb 27 2019

PROG

(PARI) for(n=0, 1500, if(!A177894(n), print1(n, ", "))) \\ See A177894 for its program

CROSSREFS

Cf. A177894, A239019, A317291.

Sequence in context: A071273 A226467 A244394 * A115853 A050785 A239019

Adjacent sequences:  A299789 A299790 A299791 * A299793 A299794 A299795

KEYWORD

nonn,base

AUTHOR

Jianing Song, Jan 21 2019

STATUS

approved

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Last modified May 22 14:32 EDT 2019. Contains 323480 sequences. (Running on oeis4.)