A060646 Bonse sequence: a(n) = minimal j such that n-j+1 < prime(j).

1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18

Offset: 1

Author

Frank Ellermann, Apr 17 2001

Keywords

• easy
• nonn
• nice

Comments

For 35.

Examples

			For n=5, j=3 gives 5-3+1 = 3 < prime(3) = 5, true; but if j=2 we get 5-2+1 = 4 which is not < prime(2) = 3; hence a(5) = 3.
a(75)=18 because 75-18+1=58 < 61=prime(18), but 75-17+1=59=prime(17).
		

References

• R. Remak, Archiv d. Math. u. Physik (3) vol. 15 (1908) 186-193

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• H. Bonse, Über eine bekannte Eigenshaft der Zahl 30 und ihre Verallgemeinerung, Archiv d. Math. u. Physik (3) vol. 12 (1907) 292-295.
• H. Rademacher and O. Toeplitz, Eine Eigenschaft der Zahl 30, (A property of the number 30), Von Zahlen und Figuren (1930, reprint Springer 1968), ch. 22.

Crossrefs

Cf. A014688.

Programs

Haskell

import Data.List (findIndex)
import Data.Maybe (fromJust)
a060646 n = (fromJust $ findIndex ((n+1) <) a014688_list) + 1
-- Reinhard Zumkeller, Sep 16 2011

Mathematica

Table[j=0; While[j++; n-j+1 >= Prime[j]]; j, {n, 1, 76}] (* Jean-François Alcover, Aug 30 2011 *)

Python

from sympy import nextprime
from itertools import count, islice
def agen(): # generator of terms
    n, pj = 1, 2
    for j in count(1):
        while n - j + 1 < pj: yield j; n += 1
        pj = nextprime(pj)
print(list(islice(agen(), 76))) # Michael S. Branicky, Aug 09 2022