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

1,1

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

Mathematica

Select[Range[162], !IntegerQ[Log2[#]] && Sum[Boole[IntegerQ[Log2[FromDigits[Drop[IntegerDigits[#], i]]]]], {i, IntegerLength[#]}] > 0 &]
(* Alternative: *)
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 *)

Prog

(PARI) isp2(k) = k==1<<valuation(k, 2); \\ 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

Crossrefs

Cf. A007524, A057716, A209229.

Complement of A000079 in A385289.

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

Sequence in context: A182404 A234021 A264023 * A177902 A108722 A246139

Adjacent sequences: A384711 A384712 A384713 * A384715 A384716 A384717

Keyword

nonn,base,easy

Author

Stefano Spezia, Jun 23 2025

Status

approved