

A229489


Conjecturally, possible differences between prime(k)^2 and the next prime for some k.


1



1, 2, 4, 6, 10, 12, 16, 18, 22, 24, 28, 30, 34, 36, 40, 42, 46, 48, 52, 54, 58, 60, 64, 66, 70, 72, 76, 78, 82, 84, 88, 90, 94, 96, 100, 102, 106, 108, 112, 114, 118, 120, 124, 126, 130, 132, 136, 138, 142, 144, 148, 150, 154, 156, 160, 162, 166, 168, 172, 174
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OFFSET

1,2


COMMENTS

Are there any missing terms? The first 10^7 primes were examined. All these differences occur for some k < 10^5. Note that the first differences of these terms is 1, 2, or 4.
The similarity to A047233 is understood by a comment in A091666.  R. J. Mathar, Oct 28 2013


LINKS

Table of n, a(n) for n=1..60.


MATHEMATICA

t = Table[p2 = Prime[k]^2; NextPrime[p2]  p2, {k, 100000}]; Take[Union[t], 60]


CROSSREFS

Cf. A000040 (primes), A001248 (primes squared).
Cf. A004277 (conjecturally, possible gaps between adjacent primes).
Cf. A091666 (prime greater than prime(n)^2).
Cf. A229488 (possible differences between prime(k)^2 and the previous prime).
Sequence in context: A132631 A248614 A105965 * A107304 A082417 A161842
Adjacent sequences: A229486 A229487 A229488 * A229490 A229491 A229492


KEYWORD

nonn


AUTHOR

T. D. Noe, Oct 21 2013


STATUS

approved



