A032749 - OEIS

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

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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