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A330593 Positive integers not occurring in A330614 (subsequence of first differences with indices of primes gives back the original). 2
2, 3, 7, 12, 15, 17, 20, 21, 25, 26, 27, 32, 34, 35, 36, 39, 40, 42, 51, 52, 56, 57, 58, 62, 63, 64, 65, 69, 70, 72, 76, 77, 80, 81, 82, 86, 87, 88, 90, 91, 92, 93, 94, 95, 99, 100, 104, 105, 106, 110, 111, 112, 115, 116, 117, 122, 125, 128, 130, 133, 134, 135, 140, 141, 142, 145, 146, 147, 148, 154, 155, 156, 158, 159, 160, 161, 162, 164, 165, 168, 169, 171, 172, 175, 176, 177, 178 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence A330614 has an interesting "fractal" structure of interleaved subsequences. It is computed in a nearly greedy manner as the lexicographically smallest sequence of distinct terms which has a certain property. One might expect that this yields a permutation of the positive integers, but it turns out that some numbers will never occur. These are listed here, in the hope that more can be found out about this subset.

While the first terms are isolated, the sequence appears to have a density of > 3/5 already around n = 500, 2/3 around n = 1500, and almost 3/4 near n = 2*10^4. Is this the limiting density, or is it asymptotically increasing to a larger value?

LINKS

M. F. Hasler, Table of n, a(n) for n = 1..18900: terms that can be deduced from A330614(1..10^4).

M. F. Hasler, Plot of the density averaged over sqrt(a(n)) terms, Dec 30 2019.

PROG

(PARI) A=setminus([1..2*#A330614], Set(A330614)) \\ with a sufficiently large vector A330614.

CROSSREFS

Complement of the range of A330614 in the positive integers A000027.

Sequence in context: A191704 A284903 A259226 * A275374 A168249 A080140

Adjacent sequences:  A330590 A330591 A330592 * A330594 A330595 A330596

KEYWORD

nonn

AUTHOR

M. F. Hasler, Dec 27 2019

STATUS

approved

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Last modified September 18 16:22 EDT 2020. Contains 337170 sequences. (Running on oeis4.)