A344344 Starts of runs of 4 consecutive Gray-code Niven numbers (A344341).

1, 6, 30, 126, 510, 543, 783, 903, 2046, 2093, 3773, 3903, 7133, 7743, 8190, 8223, 8703, 10087, 12303, 12543, 14343, 14463, 15423, 15903, 16143, 16263, 20167, 22687, 27727, 30247, 30653, 30783, 32766, 35629, 40327, 47509, 47887, 49133, 50407, 57533, 60071, 60487

Offset: 1

Author

Amiram Eldar, May 15 2021

Keywords

• nonn
• base

Comments

Are there 5 consecutive Gray-code Niven numbers? There are no such numbers below 10^10.

Examples

			1 is a term since 1, 2, 3 and 4 are all Gray-code Niven numbers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005811, A014550.

Subsequence of A344341, A344342 and A344343.

Similar sequences: A141769 (decimal), A328207 (factorial), A328211 (Zeckendorf), A328215 (lazy Fibonacci), A330933 (binary), A334311 (base phi), A331824 (negabinary), A342429 (base 3/2).

Programs

Mathematica

gcNivenQ[n_] := Divisible[n, DigitCount[BitXor[n, Floor[n/2]], 2, 1]]; Select[Range[60000], AllTrue[# + {0, 1, 2, 3}, gcNivenQ] &]