A371444 Numbers whose binary indices are composite numbers.

8, 32, 40, 128, 136, 160, 168, 256, 264, 288, 296, 384, 392, 416, 424, 512, 520, 544, 552, 640, 648, 672, 680, 768, 776, 800, 808, 896, 904, 928, 936, 2048, 2056, 2080, 2088, 2176, 2184, 2208, 2216, 2304, 2312, 2336, 2344, 2432, 2440, 2464, 2472, 2560, 2568

Offset

1,1

Comments

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

Links

Table of n, a(n) for n=1..49.

Example

The terms together with their binary expansions and binary indices begin:
     8:           1000 ~ {4}
    32:         100000 ~ {6}
    40:         101000 ~ {4,6}
   128:       10000000 ~ {8}
   136:       10001000 ~ {4,8}
   160:       10100000 ~ {6,8}
   168:       10101000 ~ {4,6,8}
   256:      100000000 ~ {9}
   264:      100001000 ~ {4,9}
   288:      100100000 ~ {6,9}
   296:      100101000 ~ {4,6,9}
   384:      110000000 ~ {8,9}
   392:      110001000 ~ {4,8,9}
   416:      110100000 ~ {6,8,9}
   424:      110101000 ~ {4,6,8,9}
   512:     1000000000 ~ {10}
   520:     1000001000 ~ {4,10}
   544:     1000100000 ~ {6,10}
   552:     1000101000 ~ {4,6,10}
   640:     1010000000 ~ {8,10}
   648:     1010001000 ~ {4,8,10}
   672:     1010100000 ~ {6,8,10}

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[100], EvenQ[#]&&And@@Not/@PrimeQ/@bpe[#]&]

Crossrefs

For powers of 2 instead of composite numbers we have A253317.

For prime indices we have the even case of A320628.

For prime instead of composite we have A326782.

This is the even case of A371444.

An opposite version is A371449.

A000040 lists prime numbers, complement A018252.

A000961 lists prime-powers.

A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.

A070939 gives length of binary expansion.

A096111 gives product of binary indices.

Cf. A001222, A005117, A055887, A320629, A326781, A368109, A368533, A371289, A371452.

Sequence in context: A322056 A059880 A144096 * A127988 A371454 A129749

Adjacent sequences: A371441 A371442 A371443 * A371445 A371446 A371447

Keyword

nonn

Author

Gus Wiseman, Mar 30 2024

Status

approved