A032746 - OEIS

%I #19 Jul 18 2024 08:55:16

%S 27257,272570,302693,323576,364509,502785,513675,537771,676657,678146,

%T 731378,831122,836553,913797,920456,921269,1045361,1144983,1169054,

%U 1283069,1288697,1292673,1343642,1346117,1472078,1523993,1640026

%N Super-6 Numbers (6 * n^6 contains substring '666666' in its decimal expansion).

%C The terms a({5, 9, 11, 12}) = {364509, 676657, 731378, 831122} are such that 6*a(n)^6 == 66666646, 66666694, or 66666624 (mod 10^8). Therefore, any number congruent to one of these (mod 5*10^7) is also in the sequence. Of course, for any term a(n), all numbers a(n)*10^k, k >= 0, are also in the sequence. - _M. F. Hasler_, Jul 16 2024

%D C. A. Pickover, "Keys to Infinity", New York: Wiley, p. 7, 1995.

%H Giovanni Resta, <a href="https://www.numbersaplenty.com/set/super-d_number/">super-d numbers</a>, personal web site "Numbers Aplenty", 2013

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Super-dNumber.html">Super-d Number.</a>

%t With[{c=6},Select[Range[165*10^4],SequenceCount[IntegerDigits[c #^c],PadRight[ {},c,c]]>0&]] (* _Harvey P. Dale_, Jan 18 2023 *)

%o (PARI) select( {is_A032746(n)=is_A014569(n,6)}, [1..10^5])

%o for(n=1, oo, is_A032746(n)&& print1(n", ")) \\ Quite slow... - _M. F. Hasler_, Jul 16 2024

%Y Cf. A014569 (d=3), A032743 - A032749 (d=2, ..., 9).

%K nonn,base

%O 1,1

%A _Patrick De Geest_, May 15 1998

%E Offset changed to 1 by _M. F. Hasler_, Jul 16 2024