

A309916


a(n) = N^(1/4) * log(N) / sqrt(log(log(N))) rounded to nearest integer, with N=2^n. Related to operation count of the deterministic factorization of an integer N using an improved PollardStrassen method.


1



3, 4, 5, 7, 10, 13, 17, 22, 28, 36, 46, 58, 73, 91, 114, 143, 178, 221, 274, 338, 418, 516, 635, 781, 959, 1177, 1443, 1766, 2161, 2641, 3225, 3936, 4800, 5849, 7123, 8669, 10545, 12819, 15576, 18916, 22961, 27859, 33786, 40958, 49631, 60119, 72795, 88113, 106618
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OFFSET

2,1


COMMENTS

The article by Costa and Harvey provides an improved unconditional deterministic complexity bound for computing the prime factorization of an integer N as O(M_int(N^(1/4)*log(N)/sqrt(log(log(N))))), where M_int(k) denotes the cost of multiplying kbit integers. The sequence shows values of the M_int argument for N=2^n.


LINKS

Table of n, a(n) for n=2..50.
Edgar Costa, David Harvey, Faster deterministic integer factorization, arXiv:1201.2116v1 [math.NT] 10 Jan 2012.
Edgar Costa, David Harvey, Faster deterministic integer factorization, Math. Comp. 83 (2014), 339345.


PROG

(PARI) cn(N)=N^0.25*log(N)/sqrt(log(log(N)));
for(k=2, 50, print1(round(cn(2^k)), ", "))


CROSSREFS

Cf. A309917.
Sequence in context: A288451 A236384 A073957 * A162311 A003312 A022440
Adjacent sequences: A309913 A309914 A309915 * A309917 A309918 A309919


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Aug 23 2019


STATUS

approved



