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

10, 224, 278, 286, 452, 473, 502, 510, 645, 656, 698, 744, 871, 889, 909, 921, 955, 960, 966, 972, 1010, 1062, 1086, 1113, 1121, 1163, 1182, 1200, 1201, 1208, 1271, 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

Offset

1,1

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Example

The last few digits of 2^224 are 610249216. They contain 1024 as a substring.

Maple

filter:= n -> StringTools:-Search("1024", sprintf("%d", 2^n)) > 0:
select(filter, [$1..2000]); # Robert Israel, Mar 16 2021

Mathematica

Select[Range[2000], StringContainsQ[ToString[2^#], ToString[2^10]] &]
Select[Range[2000], SequenceCount[IntegerDigits[2^#], {1, 0, 2, 4}]>0&] (* Harvey P. Dale, Dec 15 2024 *)

Prog

(PARI) isok(k) = #strsplit(Str(2^k), Str(2^10)) > 1; \\ Michel Marcus, Mar 16 2021
(Python)
A342601_list, k, m, s = [], 1, 2, str(2**10)
while k < 10**6:
    if s in str(m):
        A342601_list.append(k)
    k += 1
    m *= 2 # Chai Wah Wu, Mar 17 2021

Crossrefs

Cf. A000079, A046296.

Sequence in context: A223817 A317171 A229256 * A361149 A052789 A092254

Adjacent sequences: A342598 A342599 A342600 * A342602 A342603 A342604

Keyword

nonn,base

Author

Tanya Khovanova, Mar 16 2021

Status

approved