

A222030


Primes and quartersquares.


2



0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 16, 17, 19, 20, 23, 25, 29, 30, 31, 36, 37, 41, 42, 43, 47, 49, 53, 56, 59, 61, 64, 67, 71, 72, 73, 79, 81, 83, 89, 90, 97, 100, 101, 103, 107, 109, 110, 113, 121, 127, 131, 132, 137, 139, 144, 149, 151, 156, 157, 163, 167, 169
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OFFSET

0,3


COMMENTS

Union of A002620 and A000040.
It appears that there is always a prime between two consecutive quarter squares, if n >= 2. Therefore in a square spiral, or zigzag, whose vertices are the quartersquares, it appears that there is always a prime between two consecutive vertices, if n >= 2.
Apparently the above comment is equivalent to the Oppermann's conjecture.  Omar E. Pol, Oct 26 2013
Union of A000040 and A000290 and A002378.  Omar E. Pol, Oct 28 2013


LINKS

Table of n, a(n) for n=0..63.
Wikipedia, Oppermann's conjecture


FORMULA

a(n) ~ n log n.  Charles R Greathouse IV, Mar 04 2013


MATHEMATICA

mx = 13; Union[Prime[Range[PrimePi[mx^2]]], Floor[Range[2*mx]^2/4]] (* Alonso del Arte, Mar 03 2013 *)


CROSSREFS

Cf. A000040, A002620, A000290, A014085, A220492, A220506, A220508, A220516.
Sequence in context: A234853 A060863 A063934 * A062490 A211543 A180711
Adjacent sequences: A222027 A222028 A222029 * A222031 A222032 A222033


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Feb 05 2013


STATUS

approved



