cp's OEIS Frontend

A055600 Numbers of form 2^i*3^j + 1 with i, j >= 0.

%I A055600 #28 Sep 16 2024 12:47:16
%S A055600 2,3,4,5,7,9,10,13,17,19,25,28,33,37,49,55,65,73,82,97,109,129,145,
%T A055600 163,193,217,244,257,289,325,385,433,487,513,577,649,730,769,865,973,
%U A055600 1025,1153,1297,1459,1537,1729,1945,2049,2188,2305,2593,2917,3073,3457,3889
%N A055600 Numbers of form 2^i*3^j + 1 with i, j >= 0.
%C A055600 If X is an n-set and Y a fixed (n-5)-subset of X then a(n-5) is equal to the number of 2-subsets of X intersecting Y. - _Milan Janjic_, Aug 15 2007
%H A055600 Amiram Eldar, <a href="/A055600/b055600.txt">Table of n, a(n) for n = 1..1000</a>
%H A055600 Graham Everest, Peter Rogers, and Thomas Ward, <a href="https://doi.org/10.1007/3-540-45455-1_8">A higher-rank Mersenne problem</a>, Algorithmic Number Theory: 5th International Symposium, ANTS-V Sydney, Australia, July 7-12, 2002 Proceedings 5, Lect. Notes Computer Sci. 2369, Springer Berlin Heidelberg, 2002, pp. 95-107; <a href="https://durham-repository.worktribe.com/preview/1654492/10053.pdf">alternative link</a>.
%H A055600 Milan Janjić, <a href="https://citeseerx.ist.psu.edu/document?repid=rep1&amp;type=pdf&amp;doi=801b6b226bfe1d6b002fb4946c3957d7052132bd">Two Enumerative Functions</a>.
%F A055600 a(n) = A003586(n) + 1.
%e A055600 a(7) = 13 since 13 = 2^2 * 3^1 + 1.
%t A055600 mx = 4000; Sort@ Flatten@ Table[ 2^i*3^j + 1, {i, 0, Log[2, mx]}, {j, 0, Log[3, mx/2^i]}] (* _Robert G. Wilson v_, Aug 17 2012 *)
%o A055600 (PARI) is(k) = if(k == 2, 1, k > 2 && vecmax(factor(k - 1, 5)[, 1]) < 5); \\ _Amiram Eldar_, Sep 02 2024
%o A055600 (Python)
%o A055600 from sympy import integer_log
%o A055600 def A055600(n):
%o A055600     def bisection(f,kmin=0,kmax=1):
%o A055600         while f(kmax) > kmax: kmax <<= 1
%o A055600         while kmax-kmin > 1:
%o A055600             kmid = kmax+kmin>>1
%o A055600             if f(kmid) <= kmid:
%o A055600                 kmax = kmid
%o A055600             else:
%o A055600                 kmin = kmid
%o A055600         return kmax
%o A055600     def f(x): return n+x-sum((x//3**i).bit_length() for i in range(integer_log(x,3)[0]+1))
%o A055600     return bisection(f,n,n)+1 # _Chai Wah Wu_, Sep 15 2024
%Y A055600 Primes in this sequence give A005109 (Class 1- or Pierpoint primes).
%Y A055600 Cf. A003586.
%K A055600 easy,nonn
%O A055600 1,1
%A A055600 _Henry Bottomley_, Jun 01 2000
%E A055600 Offset corrected by _Amiram Eldar_, Sep 02 2024