A277079 Least number k for which k^n contains n as a substring and n^k contains k as a substring.

1, 35, 7, 61, 5, 6, 3, 7, 5, 10, 11, 15, 6, 36, 7, 16, 17, 33, 16, 44, 6, 48, 36, 3, 5, 9, 31, 8, 32, 69, 8, 5, 8, 5, 2, 2, 9, 8, 6, 6, 5, 8, 7, 6, 6, 9, 8, 6, 2, 7, 2, 8, 6, 5, 5, 5, 3, 8, 9, 6, 4, 3, 6, 6, 6, 25, 5, 6, 3, 6, 3, 3, 2, 6, 5, 6, 3, 7, 8, 7, 4, 2

Offset: 1

Author

Paolo P. Lava, Sep 28 2016

Keywords

• nonn
• base
• easy

Comments

a(n) = n for 1, 5, 6, 10, 11, 16, 17.

Records for a(1) = 1, a(2) = 35, a(4) = 61, a(30) = 69, a(1061) = 84, a(1256) = 91, ...

Examples

			2^35 = 34359738368 and 35 is a substring;
35^2 = 1225 and 2 is a substring.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A061280.

Programs

Maple

P:=proc(q) local a,b,j,k,n,ok; for n from 1 to q do a:=convert(n,string); ok:=1; for k from 1 to q do if ok=1 then if searchtext(a,convert(k^n,string))>0 then b:=convert(k,string);
for j from 1 to q do if searchtext(b,convert(n^k,string))>0 then print(k); ok:=0; break; fi; od; fi; fi; od; od; end: P(10^3);

Mathematica

Table[k = 1; While[Or[Length@ SequencePosition[IntegerDigits[k^n], IntegerDigits[n]] == 0, Length@ SequencePosition[IntegerDigits[n^k], IntegerDigits[k]] == 0], k++]; k, {n, 120}] (* Michael De Vlieger, Sep 28 2016, Version 10.1 *)