A032749 Super-9 Numbers (9*n^9 contains substring '999999999' in its decimal expansion).

17546133, 32613656, 93568867, 107225764, 109255734, 113315082, 121251742, 175461330, 180917907, 182557181, 190215626, 227366552, 267791979, 297981691, 298002027, 301321202, 321541434, 326136560, 326687646, 329178946, 351038353

Offset

1,1

Comments

The smallest super-9 prime is 182557181.

For any term a(n), all numbers a(n)*10^k, k >= 0, are also in the sequence. - M. F. Hasler, Jul 16 2024

Probably has density 1. In any case it has positive lower density since 10^12*k + 93568867 is in the sequence for all k > 0. This also shows there are infinitely many primes (with positive lower relative density in the primes) in this sequence. - Charles R Greathouse IV, Jul 17 2024

References

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

Links

Table of n, a(n) for n=1..21.

Giovanni Resta, super-d numbers, personal web site "Numbers Aplenty", 2013

Eric Weisstein's World of Mathematics, Super-d Number.

Example

17546133^9 = 157627777777777302658446998030642098243159192883927973928032212853, and upon multiplication by 9, since 7...77*9 = 69...93, the string of 10 '7's becomes a string with 9 consecutive '9's. Hence 17546133 is in the sequence.

Crossrefs

Cf. A014569, A032743-A032748.

Sequence in context: A326137 A288078 A183269 * A235848 A250981 A344631

Adjacent sequences: A032746 A032747 A032748 * A032750 A032751 A032752

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998; extended Feb 22 2004

Status

approved