A384714 Nonpowers of 2 whose trailing digits form a power of 2.

11, 12, 14, 18, 21, 22, 24, 28, 31, 34, 38, 41, 42, 44, 48, 51, 52, 54, 58, 61, 62, 68, 71, 72, 74, 78, 81, 82, 84, 88, 91, 92, 94, 98, 101, 102, 104, 108, 111, 112, 114, 116, 118, 121, 122, 124, 131, 132, 134, 138, 141, 142, 144, 148, 151, 152, 154, 158, 161, 162

Offset: 1

Author

Stefano Spezia, Jun 23 2025

Keywords

• nonn
• base
• easy

Comments

Nonpowers of 2 that are of the form h*10^j + 2^k with j > k*log10(2) and h > 0.

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007524, A057716, A209229.

Complement of A000079 in A385289.

A002275 \ {0, 1} and A017281 \ {1} are subsequences.

Programs

Mathematica

Select[Range[162], !IntegerQ[Log2[#]] && Sum[Boole[IntegerQ[Log2[FromDigits[Drop[IntegerDigits[#],i]]]]],{i,IntegerLength[#]}] > 0 &]
(* Second program: *)
nn = 162; s = 2^Range[0, Floor@ Log2[nn]]; Complement[Union@ Reap[Map[(w = IntegerDigits[#]; i = 1; While[Set[k, FromDigits@Join[IntegerDigits[i], w]] <= nn, Sow[k]; i++]) &, s] ][[-1, 1]], s] (* Michael De Vlieger, Jun 25 2025 *)

PARI

isp2(k) = k==1<A209229
isok(k) = if (!isp2(k), for (i=1, oo, my(z=k % 10^i); if (z==k, return(0), if (z && isp2(z), return(1))))); return(0); \\ Michel Marcus, Jun 24 2025