A158930 -id:A158930 - cp's OEIS frontend

A158928 a(n) is the smallest integer not yet in the sequence with no common base-3 digit with a(n-1).

1, 2, 3, 8, 4, 6, 13, 18, 40, 20, 121, 24, 364, 26, 9, 80, 10, 242, 12, 728, 27, 2186, 28, 6560, 30, 19682, 31, 59048, 36, 177146, 37, 531440, 39, 1594322, 81, 4782968, 82, 14348906, 84, 43046720, 85, 129140162, 90, 387420488, 91, 1162261466, 93

Offset: 1

R. J. Mathar, Mar 31 2009

Numbers of A031944 do not appear in this sequence. After a number which has base-3 digits 0 and 1, a number of the form 3^k-1 (see A024023) follows by definition, because its base-3 digits are all 2.

			The 4th term cannot be 4 because 4(base10)=11(base3) shares a common digit 1 with a(3)=3(base10)=10(base3). It cannot be 5(base10)=12(base3) because this shares the digit 1 with 3=10(base3). It cannot be 6(base10)=20(base3) because this shares the digit 0 with 3=10(base3). It cannot be 7(base10)=21(base3) because this shares the digit 1 with 3=10(base3). It becomes a(4)=8(base10)=22(base3) which does not have the digit 0 or 1 of a(3)=10(base3).

Cf. A067581 (base-10), A158929 (base-4), A158930 (base-5).

A158929 a(n) is the smallest integer not yet in the sequence with no common base-4 digit with a(n-1).

Original entry on oeis.org

1, 2, 3, 4, 10, 5, 8, 7, 32, 13, 34, 15, 6, 12, 9, 48, 21, 11, 16, 14, 17, 42, 19, 170, 20, 43, 64, 46, 65, 47, 68, 58, 69, 59, 80, 62, 81, 63, 18, 255, 22, 51, 25, 60, 26, 192, 37, 195, 38, 204, 41, 207, 85, 35, 341, 40, 23, 128, 29, 130, 31, 136, 53, 138, 55, 160, 61, 162

Offset: 1

R. J. Mathar, Mar 31 2009

Numbers of A031945 do not appear in this sequence.

			The fifth term cannot be 5(base10)=11(base4), 6(base10)=12(base4), 7(base10)=13(base4), 8(base10)=20(base4) or 9(base10)=21(base4) because each of them has either a 0 or a 1 in its base-4 representation, which it would have in common with 4(base10)=10(base4). So a(5)=10(base10)=22(base4) which displays only digits of 2 in base 4.

Cf. A067581 (base-10), A158928 (base-3), A158930 (base-5).

cp's OEIS Frontend

A158928 a(n) is the smallest integer not yet in the sequence with no common base-3 digit with a(n-1).

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