A057450 Prime recurrence: a(n+1) = a(n)-th prime, with a(1) = 4.

4, 7, 17, 59, 277, 1787, 15299, 167449, 2269733, 37139213, 718064159, 16123689073, 414507281407, 12055296811267, 392654585611999, 14199419938376521, 565855918431234443

Offset: 1

Author

Robert G. Wilson v, Sep 26 2000

Keywords

• nonn
• hard
• more

Comments

Lubomir Alexandrov informs me that he studied this sequence in his 1965 notebook. - N. J. A. Sloane, May 23 2008

References

• Alexandrov, Lubomir. "On the nonasymptotic prime number distribution." arXiv preprint math/9811096 (1998). (See Appendix.)

Links

• Lubomir Alexandrov, Prime Number Sequences And Matrices Generated By Counting Arithmetic Functions, Communications of the Joint Institute of Nuclear Research, E5-2002-55, Dubna, 2002.

Crossrefs

Cf. A007097.

Programs

Mathematica

NestList[ Prime, 4, 13 ]

Python

from sympy import prime
from itertools import accumulate
def f(an, _): return prime(an)
print(list(accumulate([4]*12, f))) # Michael S. Branicky, Apr 07 2021

Extensions

a(15)-a(17) from Robert G. Wilson v, Mar 07 2017 using Kim Walisch's primecount