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

Author

Antti Karttunen, Jul 22 2014

Keywords

• nonn
• more

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.

Examples

			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.
		

Crossrefs

A048674 is a subsequence.

Cf. A048673, A064216, A245447, A245448.

Programs

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))

Extensions

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