A229489 Conjecturally, possible differences between prime(k)^2 and the next prime for some k.

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

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]
NextPrime[#]-#&/@(Prime[Range[100000]]^2)//Union (* Harvey P. Dale, Apr 19 2020 *)

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 * A355643 A107304 A082417

Adjacent sequences: A229486 A229487 A229488 * A229490 A229491 A229492

Keyword

nonn

Author

T. D. Noe, Oct 21 2013

Status

approved