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

Author

Eder Vanzei, Oct 14 2019

Keywords

• nonn
• easy
• base

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

Examples

			16777216 = 2^24.
		

Links

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

Crossrefs

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

Programs

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 *)

Python

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