A246280 a(n) = the smallest starting value for k such that n will be the exact number of additional iterations of A003961 needed when we start from A003961(k) before we first reach a number of the form 4k+1; the least k such that A246271(k) = n.

1, 2, 5, 66, 91, 55, 21, 46, 1362, 1654, 1419, 574, 6463, 5263, 4607, 3497, 589843, 430261, 574823, 567583, 554111, 545869, 20490043, 14635735, 8781429

Offset

0,2

Comments

The sequence is infinite (well-defined for all n), provided that A246271 is not bounded.

All the terms are squarefree (see the comment in A246259).

From 2 onward their prime factorizations are: 2, 5, 2*3*11, 7*13, 5*11, 3*7, 2*23, 2*3*227, 2*827, 3*11*43, 2*7*41, 23*281, 19*277, 17*271, 13*269, 571*1033, 13*23*1439, 563*1021, 557*1019, 547*1013, 541*1009, 7*2927149, 5*2927147, 3*2927143. (Note that 2927149 = A000040(211943)).

Note how A003961(21) = 55 and A003961(55) = 91. Also A003961(545869) = 554111, A003961(554111) = 567583, A003961(567583) = 574823.

Similarly: A003961(8781429) = 14635735 and A003961(14635735) = 20490043.

Apart from those descending subsections, the growth rate of the sequence should be roughly a(n) ~ 2^n, assuming that the distribution of 4k+1 (A002144) and 4k+3 primes (A002145) among the primes is even and essentially random.

Links

Table of n, a(n) for n=0..24.

Example

a(0) = 1, because 1 is the first such number >= 1 that no iterations are needed before A003961(1) (= 1) is of the form 4k+1.
a(1) = 2, because 2 is the first such number >= 1 that exactly one additional iteration of A003961 is needed before A003961(2) = 3 is of the form 4k+1; as A003961(3) = 5.
a(2) = 5, because 5 is the first such number that exactly two additional iterations of A003961 are needed before A003961(5) = 7 is of the form 4k+1; as A003961(7) = 11 and A003961(11) = 13.

Prog

(Scheme)
;; Other code as in A246259:
(define (A246280 n)  (A246259bi n 1))

Crossrefs

Leftmost column of array A246259.

A246167 gives the same sequence sorted into ascending order.

Cf. A003961, A002144, A002145, A246271, A048672.

Sequence in context: A086560 A305292 A268211 * A333165 A133004 A321602

Adjacent sequences: A246277 A246278 A246279 * A246281 A246282 A246283

Keyword

nonn

Author

Antti Karttunen, Aug 22 2014

Status

approved