cp's OEIS Frontend

A229629 Numbers k such that k is in the middle of decimal expansion of k^k.

%I A229629 #26 Nov 21 2021 13:36:01
%S A229629 1,6,888,1808,2138,65246,268105
%N A229629 Numbers k such that k is in the middle of decimal expansion of k^k.
%C A229629 a(6) is greater than 50000.
%C A229629 a(8) > 600000. - _Giovanni Resta_, Oct 08 2013
%e A229629 6 is in the sequence because 6^6 = 46656, which includes a 6 in the middle.
%e A229629 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.
%t A229629 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}]
%o A229629 (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
%o A229629 (Python)
%o A229629 from itertools import islice
%o A229629 def A229629(): # generator of terms
%o A229629     n = 1
%o A229629     while True:
%o A229629         s, sn = str(n**n), str(n)
%o A229629         l, ln = len(s), len(sn)
%o A229629         if (ln-l) % 2 == 0 and s[l//2-ln//2:l//2+(ln+1)//2] == sn: yield n
%o A229629         n += 1
%o A229629 A229629_list = list(islice(A229629(),5)) # _Chai Wah Wu_, Nov 21 2021
%Y A229629 Cf. A033147, A049329, A131495.
%K A229629 nonn,base,nice,more
%O A229629 1,2
%A A229629 _Farideh Firoozbakht_, Oct 04 2013
%E A229629 a(6)-a(7) from _Giovanni Resta_, Oct 08 2013