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A177928 Let n be the number whose square n^2 has the decimal expansion { d(1) d(2) ... d(D) }, and let q be the corresponding number whose decimal expansion is { d(2) d(3) ... d(D) d(1)}. Sequence lists numbers n dividing q. 2
1, 2, 3, 9, 27, 33, 66, 99, 123, 246, 271, 333, 351, 407, 429, 462, 481, 518, 546, 567, 666, 693, 702, 715, 777, 814, 819, 924, 936, 999, 1434, 2151, 2868, 3333, 4521, 4818, 6666, 7227, 7373, 7535, 8631, 9042, 9999, 33333, 53658, 54546, 66666, 80487, 81819 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A178028 is a subsequence of this sequence.

When n divides q, n divides d(D)*(10^D - 1) because q = 10*n^2 - d(D)*(10^D - 1). If n is prime, n divides (10^D - 1); for example, the prime term 271 divides 10^5 - 1 = 99999 = 271*369.

LINKS

Table of n, a(n) for n=1..49.

Eric Weisstein's World of Mathematics, Repunits

EXAMPLE

429 is in the sequence because 429^2 = 184041 and 840411/429 = 1959.

MAPLE

for n from 1 to 10^6 do: d:=convert(n^2, base, 10):n1:=nops(d):s:=sum('d[i]*10^i', 'i'=1..n1-1)+d[n1]:if irem(s, n)=0 then printf(`%d, `, n):else fi:od:

MATHEMATICA

Select[Range[100000], Mod[FromDigits[RotateLeft[IntegerDigits[#^2]]], #] == 0 &] (* T. D. Noe, Jul 27 2012 *)

CROSSREFS

Cf. A002275, A003020, A005422, A067063, A102380, A178028.

Sequence in context: A038523 A096237 A309814 * A057231 A178028 A045596

Adjacent sequences:  A177925 A177926 A177927 * A177929 A177930 A177931

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, May 15 2010

STATUS

approved

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Last modified October 1 13:04 EDT 2020. Contains 337443 sequences. (Running on oeis4.)