A324798 a(n) = floor(sqrt(2)*prime(n)) - prime(n+1).

-1, -1, 0, -2, 2, 1, 5, 3, 3, 10, 6, 11, 14, 13, 13, 15, 22, 19, 23, 27, 24, 28, 28, 28, 36, 39, 38, 42, 41, 32, 48, 48, 54, 47, 59, 56, 59, 63, 63, 65, 72, 64, 77, 75, 79, 70, 75, 88, 92, 90, 90, 96, 89, 97, 100, 102, 109, 106, 110, 114, 107, 107, 123, 126, 125, 117, 131, 129, 141, 140, 140, 140, 146, 148, 152, 152

Offset

1,4

Comments

Theorem: a(n) > 0 for all n > 4.

References

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.18, p. 247.

Links

Table of n, a(n) for n=1..76.

Mathematica

Floor[Sqrt[2]#[[1]]]-#[[2]]&/@Partition[Prime[Range[80]], 2, 1] (* Harvey P. Dale, Nov 23 2023 *)

Crossrefs

Cf. A064051.

Sequence in context: A134226 A184050 A367094 * A226059 A353738 A127742

Adjacent sequences: A324795 A324796 A324797 * A324799 A324800 A324801

Keyword

sign

Author

N. J. A. Sloane, Sep 11 2019

Status

approved