

A122556


Primes occur infinitely often, with first appearance in order. Between each occurrence of a prime p, there are p distinct primes.


0



2, 3, 5, 2, 7, 3, 2, 11, 13, 2, 3, 5, 2, 17, 3, 2, 19, 7, 2, 3, 5, 2, 23, 3, 2, 29, 31, 2, 3, 5, 2, 37, 3, 2, 7, 11, 2, 3, 5, 2, 41, 3, 2, 43, 13, 2, 3, 5, 2, 7, 3, 2, 47, 53, 2, 3, 5, 2, 59, 3, 2, 61, 7, 2, 3, 5, 2, 11, 3, 2, 17, 67, 2, 3, 5, 2, 71, 3, 2, 7, 19, 2, 3, 5, 2, 13, 3, 2, 73, 79, 2, 3, 5
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OFFSET

1,1


COMMENTS

From a suggestion by Eric Angelini. The primes between two occurrences of p always include all smaller primes, often more than once and p  PrimePi(p) + 1 larger primes, once each. (Here PrimePi is A000720, the number of primes <= n.)


LINKS

Table of n, a(n) for n=1..93.


EXAMPLE

Between the first and 2nd 5's, the sequence is 2,7,3,2,11,13,2,3; the distinct values are {2,3,7,11,13}, a set with 5 elements.


CROSSREFS

Cf. A000720, A001511.
Sequence in context: A066949 A073481 A178094 * A175723 A084346 A165911
Adjacent sequences: A122553 A122554 A122555 * A122557 A122558 A122559


KEYWORD

easy,nonn


AUTHOR

Franklin T. AdamsWatters, Sep 20 2006


STATUS

approved



