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

1,2

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)).

Links

Table of n, a(n) for n=1..70.

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.

Example

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, ...

Prog

(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

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.

Sequence in context: A314789 A314790 A314791 * A057961 A314792 A089217

Adjacent sequences: A259565 A259566 A259567 * A259569 A259570 A259571

Keyword

nonn,base,less

Author

Sean Oneil, Jun 30 2015

Status

approved