

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
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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 nth prime appear in the sequence of first differences (A075568) not later than at the 2nth 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



