A245449 Fixed points of A245447 and A245448.

1, 2, 3, 4, 5, 9, 13, 25, 26, 30, 33, 53, 93, 1023, 1034, 1203, 1330, 2657, 8584, 17159, 779212, 970225, 1558409, 8550146, 240902643, 244608573, 325422273, 414690595, 570131490, 1020233393, 1864797542, 2438037206

Offset

1,2

Comments

First apply A003961(n), where the primes in the prime factorization of natural number n are shifted one step left [i.e. each p_i changes to p_{i+1}]. Then increment the resulting odd number by one to get an even number, which is divided by 2, and the same three operations are done second time to that quotient. This sequence consists of such numbers for which the final result is equal to the original n which we started from.

8550146 is the largest term <= 123456789.

Numbers which are in 1- and 2-cycles of A048673 and A064216.

Links

Table of n, a(n) for n=1..32.

Example

For n = 30 = 2*3*5 = p_1 * p_2 * p_3, the first shift operation results p_2 * p_3 * p_4 = 3*5*7 = 105, and (105+1)/2 = 53, which is the 16th prime, p_16. Shifting this once left results p_17 = 59, and (59+1)/2 = 30 again. Thus 30 is included in the sequence. For the same reason 53 is also included in the sequence.

Prog

(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A048673(n) = (A003961(n)+1)/2;
isA245449(n) = ((A048673(A048673(n)) == n))
i=0; for(n=1, 123456789, if(isA245449(n), i++; write("b245449.txt", i, " ", n)))
(Scheme, with Antti Karttunen's IntSeq-library)
(define A245449 (FIXED-POINTS 1 1 A245447))

Crossrefs

A048674 is a subsequence.

Cf. A048673, A064216, A245447, A245448.

Sequence in context: A107365 A026484 A120760 * A337647 A346600 A217376

Adjacent sequences: A245446 A245447 A245448 * A245450 A245451 A245452

Keyword

nonn,more

Author

Antti Karttunen, Jul 22 2014

Extensions

a(25)-a(32) added by Antti Karttunen, Sep 13 2014

Status

approved