A378894 Numbers, when written in binary, that are a proper substring of the concatenation (with repetition) in increasing order of their prime factors, when written in binary.

10, 57, 63, 355, 737, 921, 1526, 13803, 22008, 43364, 44016, 48895, 65151, 88032, 130545, 235929, 255987, 563207, 702460, 1456355, 2799617, 3020897, 3137557, 3774873, 4163463, 5697350, 5995862, 14176747, 42172441, 55933611, 87559273, 93206755, 108530173, 126474397, 180677710, 193337441, 249550095, 259779663, 533713761, 536378647, 715881440, 940339099, 1000732491

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Example

10 is a term as 10 = 1010_2 = 2 * 5 = 10_2 * 101_2 = "10101" when concatenated, which contains "1010" as a substring.
63 is a term as 63 = 111111_2 = 3 * 3 * 7 = 11_2 * 11_2 * 111_2 = "1111111" when concatenated, which contains "111111" as a substring.
1526 is a term as 1526 = 10111110110_2 = 2 * 7 * 109 = 10_2 * 111_2 * 1101101_2 = "101111101101" when concatenated, which contains "10111110110" as a substring.

Crossrefs

Cf. A027746, A378893, A376078, A372309, A371958, A371696, A372046, A371641.

Sequence in context: A200054 A034195 A351458 * A067250 A061005 A006550

Adjacent sequences: A378891 A378892 A378893 * A378895 A378896 A378897

Keyword

nonn,base

Author

Scott R. Shannon, Dec 10 2024

Status

approved