A328375 Numbers k such that the decimal expansion of 2^k contains the substring 777.

24, 40, 75, 152, 166, 179, 181, 191, 194, 199, 214, 230, 235, 260, 282, 296, 304, 311, 317, 323, 326, 332, 342, 345, 363, 370, 374, 390, 417, 424, 426, 443, 455, 468, 471, 474, 475, 483, 489, 490, 505, 512, 523, 524, 536, 540, 559, 567, 581, 584, 585, 588, 593

Offset

1,1

Comments

The decimal expansion of 2^k ends in 7776 iff k == 40 (mod 500), so the sequence is infinite. - Jon E. Schoenfield, Oct 14 2019

Conjecture: if n > 30536, then a(n) = n + 3623. - Chai Wah Wu, Oct 26 2019

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

16777216 = 2^24.

Maple

q:= n-> searchtext("777", cat(2^n))>0:
select(q, [$1..600])[];  # Alois P. Heinz, Oct 26 2019

Mathematica

aQ[n_] := SequenceCount[IntegerDigits[2^n], {7, 7, 7}] > 0; Select[Range[660], aQ] (* Amiram Eldar, Oct 26 2019 *)

Prog

(Python)
A328375_list = [k for k in range(1000) if '777' in str(2**k)] # Chai Wah Wu, Oct 26 2019

Crossrefs

Cf. A007356 (contains 666), A030000 (contains n).

Sequence in context: A211567 A316271 A357699 * A141717 A185742 A286876

Adjacent sequences: A328372 A328373 A328374 * A328376 A328377 A328378

Keyword

nonn,easy,base

Author

Eder Vanzei, Oct 14 2019

Status

approved