A256994 a(n) = n + 1 when n <= 3, otherwise a(n) = 2^(n-2) + 3; also iterates of A005187 starting from a(1) = 2.

2, 3, 4, 7, 11, 19, 35, 67, 131, 259, 515, 1027, 2051, 4099, 8195, 16387, 32771, 65539, 131075, 262147, 524291, 1048579, 2097155, 4194307, 8388611, 16777219, 33554435, 67108867, 134217731, 268435459, 536870915, 1073741827, 2147483651, 4294967299, 8589934595, 17179869187, 34359738371, 68719476739, 137438953475, 274877906947

Offset

1,1

Comments

Note that if we instead iterated function b(n) = 1+A005187(n), from b(1) onward, we would get the powers of two, A000079.

Links

Antti Karttunen, Table of n, a(n) for n = 1..128

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

If n < 4, a(n) = n + 1, otherwise a(n) = 2^(n-2) + 3 = A062709(n-2).

a(1) = 2; for n > 1, a(n) = A005187(a(n-1)).

G.f.: x*(2 - 3*x - x^2 + x^3 - 2*x^4)/((1 - x)*(1 - 2*x)). - Andrew Howroyd, Oct 29 2025

Mathematica

Table[If[n<4, n+1, 2^(n-2)+3], {n, 40}] (* Harvey P. Dale, May 14 2019 *)

Prog

(PARI)
A256994(n) = if(n < 4, n+1, 2^(n-2) + 3);
(PARI)
\\ By iterating A005187:
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
i=1; k=2; print1(k); while(i <= 40, k = A005187(k); print1(", ", k); i++);
(Scheme)
(define (A256994 n) (if (< n 4) (+ n 1) (+ (A000079 (- n 2)) 3)))
(Scheme)
;; The following uses memoization-macro definec:
(definec (A256994 n) (if (= 1 n) 2 (A005187 (A256994 (- n 1)))))

Crossrefs

Topmost row of A256995, leftmost column of A256997.

Cf. A000079, A005187, A062709, A068156.

Sequence in context: A327010 A341823 A339548 * A107481 A058521 A372266

Adjacent sequences: A256991 A256992 A256993 * A256995 A256996 A256997

Keyword

nonn

Author

Antti Karttunen, Apr 15 2015

Status

approved