cp's OEIS Frontend

A342601 Numbers k such that 2^k contains 2^10 as a substring.

%I A342601 #25 Dec 15 2024 12:00:27
%S A342601 10,224,278,286,452,473,502,510,645,656,698,744,871,889,909,921,955,
%T A342601 960,966,972,1010,1062,1086,1113,1121,1163,1182,1200,1201,1208,1271,
%U A342601 1273,1282,1315,1327,1328,1377,1431,1444,1510,1541,1550,1564,1570,1583,1610,1626,1630,1674,1677,1693,1706,1719,1720,1726,1738
%N A342601 Numbers k such that 2^k contains 2^10 as a substring.
%C A342601 This sequence includes no 1-digit numbers, only 1.111% of the 2-digit numbers, 2.111% of the 3-digit numbers, 15.744% of the 4-digit numbers, and 74.734% of the 5-digit numbers. 6-digit numbers not in the sequence become increasingly scarce. The only numbers in the interval [300000, 500000] that are not in the sequence are 304702, 328762, 329873, 344218, and 384135. Is 384135 the largest number that is not in the sequence? - _Jon E. Schoenfield_, Mar 16 2021
%H A342601 Harvey P. Dale, <a href="/A342601/b342601.txt">Table of n, a(n) for n = 1..10000</a>
%e A342601 The last few digits of 2^224 are 610249216. They contain 1024 as a substring.
%p A342601 filter:= n -> StringTools:-Search("1024",sprintf("%d",2^n)) > 0:
%p A342601 select(filter, [$1..2000]); # _Robert Israel_, Mar 16 2021
%t A342601 Select[Range[2000], StringContainsQ[ToString[2^#], ToString[2^10]] &]
%t A342601 Select[Range[2000],SequenceCount[IntegerDigits[2^#],{1,0,2,4}]>0&] (* _Harvey P. Dale_, Dec 15 2024 *)
%o A342601 (PARI) isok(k) = #strsplit(Str(2^k), Str(2^10)) > 1; \\ _Michel Marcus_, Mar 16 2021
%o A342601 (Python)
%o A342601 A342601_list, k, m, s = [], 1, 2, str(2**10)
%o A342601 while k < 10**6:
%o A342601     if s in str(m):
%o A342601         A342601_list.append(k)
%o A342601     k += 1
%o A342601     m *= 2 # _Chai Wah Wu_, Mar 17 2021
%Y A342601 Cf. A000079, A046296.
%K A342601 nonn,base
%O A342601 1,1
%A A342601 _Tanya Khovanova_, Mar 16 2021