

A229629


Numbers n such that n is in the middle of decimal expansion of n^n.


1




OFFSET

1,2


COMMENTS

a(6) is greater than 50000.
a(8) > 600000.  Giovanni Resta, Oct 08 2013


LINKS

Table of n, a(n) for n=1..7.


EXAMPLE

6 is in the sequence because 6^6 = 46656, which includes a 6 in the middle.
11 is not in the sequence, because even though the substring 11 appears twice in 11^11 = 285311670611, neither occurrence is precisely in the middle.


MATHEMATICA

Do[a = IntegerDigits[n^n]; b = Length[a]; c = IntegerLength[n]; If[EvenQ[b  c] && FromDigits[Take[a, {(b  c)/2 + 1, (b + c)/2}]] == n, Print[n]], {n, 50000}]


PROG

(PARI) is(n)=my(d=digits(n), D=digits(n^n)); if((#d+#D)%2, return(0)); for(i=1, #d, if(d[i]!=D[#D/2#d/2+i], return(0))); 1 \\ Charles R Greathouse IV, Jul 30 2016


CROSSREFS

Cf. A033147, A049329, A131495.
Sequence in context: A064430 A279304 A180992 * A137801 A076667 A000652
Adjacent sequences: A229626 A229627 A229628 * A229630 A229631 A229632


KEYWORD

nonn,base,nice,more


AUTHOR

Farideh Firoozbakht, Oct 04 2013


EXTENSIONS

a(6)a(7) from Giovanni Resta, Oct 08 2013


STATUS

approved



