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

Author

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

Keywords

• nonn
• base

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

Examples

			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.
		

References

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

Links

• Giovanni Resta, super-d numbers, personal web site "Numbers Aplenty", 2013
• Eric Weisstein's World of Mathematics, Super-d Number.

Crossrefs

Cf. A014569, A032743-A032748.