A378893 -id:A378893 - cp's OEIS frontend

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

Scott R. Shannon, Dec 10 2024

			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.

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

A378950 Numbers that are a proper substring of the concatenation (with repetition) in decreasing order of their prime factors.

Original entry on oeis.org

95, 132, 995, 9995, 73332, 85713, 93115, 131131, 197591, 632812, 999995, 4285713, 8691315, 58730137, 99999995, 131373333, 507107133, 4870313015

Offset: 1

Scott R. Shannon, Dec 11 2024

All numbers of the form 5*A055558(k), k>=1, are terms.

			95 is a term as 95 = 19 * 5 = "195" when concatenated, which contains "95" as a substring.
632812 is a term as 632812 = 563 * 281 * 2 * 2 = "56328122" when concatenated, which contains "632812" as a substring.
4870313015 is a term as 4870313015 = 748703 * 1301 * 5 = "74870313015" when concatenated, which contains "4870313015" as a substring.

Cf. A027746, A378893, A378894, A376078, A372309.

cp's OEIS Frontend

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.

Views

Author

Keywords

Examples

Crossrefs