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

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

KEYWORD

nonn,base

AUTHOR

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

STATUS

approved