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A123055 Lexicographically earliest sequence of nonprime positive integers whose first differences represent all prime numbers with exactly one appearance of each prime. 1
1, 4, 6, 25, 30, 77, 84, 95, 108, 125, 148, 177, 208, 245, 286, 329, 382, 441, 502, 573, 640, 713, 792, 875, 964, 1065, 1162, 1265, 1372, 1485, 1594, 1725, 1852, 1989, 2128, 2277, 2428, 2585, 2748, 2915, 3088, 3267, 3448, 3639, 3832, 4029, 4228, 4439, 4662 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First differences give the much older sequence A075568. - N. J. A. Sloane, Sep 26 2006

Comment from Max Alekseyev, Sep 26 2006: The n-th prime appear in the sequence of first differences (A075568) not later than at the 2n-th position. To see this it is enough to notice that in the original sequence (excluding the first element) odd and even numbers alternate. Therefore from each odd element m the sequence simply jumps to an even element m+p where p is the smallest previously unused prime.

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

The sequence S is constructed like this:

Start with "1": S = 1, ...

Add the smallest prime not added so far, in order to get a composite:

- Can we add 2? No because 1+2=3 and 3 is prime

- Can we add 3? Yes because 1+3=4 and 4 is composite

So we have now: S = 1,4, ...

Add the smallest prime not added so far in order to get a composite:

- Can we add 2? (smallest available prime); yes because 4+2=6 and 6 is composite

So we have now: S = 1,4,6, ...

- Can we add 5? No because 6+5=11 and 11 is prime

- Can we add 7? No because 6+7=13 and 13 is prime

- Can we add 11? No because 6+11=17 and 17 is prime

- Can we add 13? No because 6+13=19 and 19 is prime

- Can we add 17? No because 6+17=23 and 23 is prime

- Can we add 19? Yes because 6+19=25 and 25 is composite

So we have now: S = 1,4,6,25, ...

- Can we add 5? (smallest available prime); yes because 25+5=30 and 30 is composite

So we have now: S = 1,4,6,25,30, ...

etc.

CROSSREFS

Sequence in context: A277997 A009459 A239625 * A272306 A294996 A176858

Adjacent sequences:  A123052 A123053 A123054 * A123056 A123057 A123058

KEYWORD

base,easy,nonn

AUTHOR

Eric Angelini, Sep 26 2006

EXTENSIONS

Terms computed by Max Alekseyev.

STATUS

approved

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Last modified November 19 06:03 EST 2019. Contains 329310 sequences. (Running on oeis4.)