A032747 - OEIS

%I #23 Jul 18 2024 08:55:12

%S 140997,490996,1184321,1259609,1409970,1783166,1886654,1977538,

%T 2457756,2714763,2750425,2980991,3043607,3283057,3689639,4191601,

%U 4258476,4642725,4909960,4973029,5242829,5349973,5444788,5523544,5682065

%N Super-7 Numbers (7 * n^7 contains substring '7777777' in its decimal expansion).

%C The term a(6) = 1783166 is such that 7*a(6)^7 == 777777792 (mod 10^9). Therefore, all numbers congruent to a(6) (mod 5*10^8) are 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 Select[Range[6*10^6],MemberQ[Partition[IntegerDigits[7#^7],7,1],{7,7,7,7,7,7,7}]&] (* _Harvey P. Dale_, Sep 01 2014 *)

%o (PARI) is_A032747(n)=is_A014569(n, 7)

%o for(n=1,oo, is_A032747(n)&& print1(n", ")) \\ Quite slow, even to get the first few terms. - _M. F. Hasler_, Jul 16 2024

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

%K nonn,base

%O 1,1

%A _Patrick De Geest_, May 15 1998