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A259568 Numbers following gaps in the sequence of base-4 numbers that don't contain 0. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 6 12:35 EDT 2022. Contains 357264 sequences. (Running on oeis4.)