A080349 Costé prime expansion of Pi-e.

3, 5, 3, 23, 11, 3, 7, 5, 3, 37, 13, 11, 2, 17, 11, 3, 17, 11, 2, 29, 5, 29, 11, 3, 3, 5, 5, 479, 89, 23, 17, 11, 3, 5, 3, 7, 5, 5, 7, 5, 2, 11, 5, 3, 7, 5, 2, 5, 5, 29, 5, 5, 7, 11, 5, 7, 7, 7, 17, 5, 7, 5, 13, 23, 11, 3, 29, 23, 7, 3, 11, 3, 5, 19, 53, 19, 23, 29, 67, 1409, 347, 37, 13, 13

Offset: 0

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 2003

Keywords

• nonn
• easy

Comments

For x in (0,1], define P(x) = min{p: p prime, 1/x < p}, Phi(x) = P(x)x - 1. Costé prime expansion of x(0) is sequence a(0), a(1), ... given by x(n) = Phi(x(n-1)) (n>0), a(n) = P(x(n)) (n >= 0).

Links

• A. Costé, Sur un système fibré lié à la suite des nombres premiers, Exper. Math., 11 (2002), 383-405.

Crossrefs

Cf. A079385, A079386, A079366, A079367, A079368, A080348.

Programs

Maple

Digits := 500: P := proc(x) local y; y := ceil(evalf(1/x)); if isprime(y) then y else nextprime(y); fi; end; F := proc(x) local y,i,t1; y := x; t1 := []; for i from 1 to 100 do p := P(y); t1 := [op(t1),p]; y := p*y-1; od; t1; end; F(Pi-exp(1));