A259568 Numbers following gaps in the sequence of base-4 numbers that don't contain 0.

1, 5, 9, 13, 21, 25, 29, 37, 41, 45, 53, 57, 61, 85, 89, 93, 101, 105, 109, 117, 121, 125, 149, 153, 157, 165, 169, 173, 181, 185, 189, 213, 217, 221, 229, 233, 237, 245, 249, 253, 341, 345, 349, 357, 361, 365, 373, 377, 381, 405, 409, 413, 421, 425, 429, 437, 441, 445, 469, 473, 477, 485, 489, 493, 501, 505, 509, 597, 601, 605

Offset: 1

Author

Sean Oneil, Jun 30 2015

Keywords

• nonn
• base
• less

Comments

Partial sums for the convergent modified harmonic series in base 4 excluding 0 = Sum of 1/a(n) + 1/(a(n) + 1) + 1/(a(n) + 2) = Sum of (3*a(n)^2 + 6*a(n) + 2)/(a(n)*(a(n) + 1)*(a(n) + 2)).

Examples

			Pattern of numbers of skipped terms (numbers in base 4 with at least one zero) is 1 (4 = 10_4), 1 (8 = 20_4), 1 (12 = 30_4), 4+1 (16 = 100_4, 17 = 101_4, 18 = 102_4, 19 = 103_4, 20 = 110_4), 1, 1, 4+1, 1, 1, 4+1, 1, 1, 16+4+1, ...
		

Links

• Robert Baillie, Sums of Reciprocals of Integers Missing a Given Digit, American Mathematical Monthly (Washington, DC: Mathematical Association of America) 86 (5): 372-374, May 1979. doi:10.2307/2321096. ISSN 0002-9890. JSTOR 2321096.

Crossrefs

Subset of A016813 (congruent to 1 mod 4). a(n) = A023705(3n - 2). Each term is one more than the numbers that follow gaps in A196032.

Programs

PARI

lista(nn)=prec0 = 1; for(n=1, nn, if (vecmin(digits(n, 4)), if (prec0, print1(n,, ", ")); prec0 = 0, prec0 = 1);); \\ Michel Marcus, Aug 03 2015