A049304 Numbers k such that k is a substring of 6^k.

6, 7, 9, 13, 21, 22, 23, 29, 39, 40, 42, 44, 45, 48, 53, 55, 56, 60, 63, 64, 65, 67, 68, 69, 70, 73, 74, 75, 76, 77, 79, 82, 83, 87, 89, 92, 93, 94, 98, 105, 107, 127, 129, 131, 134, 137, 143, 147, 152, 163, 165, 167, 174, 179, 184, 189, 197, 224, 226, 227, 234, 240

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base
• easy

Examples

			9 is in the sequence because 6^9 = 10077696 contains 9 as a substring. - _David A. Corneth_, Aug 13 2021
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000400, A032740, A049301, A049302, A049303, A049305, A049306, A049307.

Programs

Mathematica

Select[Range[250],SequenceCount[IntegerDigits[6^#],IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 03 2018 *)

PARI

is(n) = { my(digs6n, digsn, streak, i, j); digs6n = digits(6^n); digsn = digits(n); for(i = 1, #digs6n + 1 - #digsn, streak = 0; for(j = 1, #digsn, if(digs6n[i + j - 1] == digsn[j], streak++ , next(2) ) ); if(streak == #digsn, return(1) ) ); 0 } \\ David A. Corneth, Aug 13 2021

Python

def ok(n): return str(n) in str(6**n)
print(list(filter(ok, range(241)))) # Michael S. Branicky, Aug 13 2021