This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A038550 #84 Feb 18 2024 02:05:11
%S A038550 3,5,6,7,10,11,12,13,14,17,19,20,22,23,24,26,28,29,31,34,37,38,40,41,
%T A038550 43,44,46,47,48,52,53,56,58,59,61,62,67,68,71,73,74,76,79,80,82,83,86,
%U A038550 88,89,92,94,96,97,101,103,104,106,107,109,112,113,116,118,122,124,127
%N A038550 Products of an odd prime and a power of two (sorted).
%C A038550 2007. For example, 37 = 18 + 19; 48 = 15 + 16 + 17; 56 = 5 + 6 + 7 + 8 + 9 + 10 + 11. (Edited by _M. F. Hasler_, Aug 29 2020: "positive" was missing here. If nonnegative integers are allowed, none of the triangular numbers 3, 6, 10, ... would be in the corresponding sequence. If negative integers are also allowed, it would only have powers of 2 (A000079) which are the only positive integers not the sum of more than one consecutive positive integers, since any x > 0 is the sum of 1-x through x.)
%C A038550 Numbers that are the difference of two triangular numbers in exactly two ways.
%C A038550 Numbers with largest odd divisor a prime number. - _Juri-Stepan Gerasimov_, Aug 16 2016
%C A038550 Numbers k for which A001222(A000265(k)) = 1. - _Antti Karttunen_, Jul 09 2020
%H A038550 T. D. Noe, <a href="/A038550/b038550.txt">Table of n, a(n) for n = 1..1000</a>
%H A038550 T. Verhoeff, <a href="https://cs.uwaterloo.ca/journals/JIS/trapzoid.html">Rectangular and Trapezoidal Arrangements</a>, J. Integer Sequences, Vol. 2, 1999, #99.1.6.
%F A038550 A001227(a(n)) = 2. - _Reinhard Zumkeller_, May 01 2012
%F A038550 a(n) ~ 0.5 n log n. - _Charles R Greathouse IV_, Apr 30 2013
%F A038550 A000265(a(n)) is a prime. - _Juri-Stepan Gerasimov_, Aug 16 2016
%F A038550 Sum_{n>=1} 1/a(n)^s = (2^s*P(s) - 1)/(2^s - 1), for s > 1, where P is the prime zeta function. - _Amiram Eldar_, Dec 19 2020
%t A038550 Select[Range[127],DivisorSigma[0,Max[Select[Divisors[#],OddQ]]]-1==1&] (* _Jayanta Basu_, Apr 30 2013 *)
%t A038550 fQ[n_] := Module[{p, e}, {p, e} = Transpose[FactorInteger[n]]; (Length[p] == 2 && p[[1]] == 2 && e[[2]] == 1) || (Length[p] == 1 && p[[1]] > 2 && e[[1]] == 1)]; Select[Range[2, 127], fQ] (* _T. D. Noe_, Apr 30 2013 *)
%t A038550 upto=150;Module[{pmax=PrimePi[upto],tmax=Ceiling[Log[2,upto]]}, Select[ Sort[ Flatten[ Outer[ Times, Prime[ Range[ 2,pmax]], 2^Range[0,tmax]]]],#<=upto&]] (* _Harvey P. Dale_, Oct 18 2013 *)
%t A038550 Flatten@Position[PrimeQ[BitShiftRight[#, IntegerExponent[#, 2]]&/@Range[#]], True]&@127 (* _Federico Provvedi_, Dec 14 2021 *)
%o A038550 (Haskell)
%o A038550 a038550 n = a038550_list !! (n-1)
%o A038550 a038550_list = filter ((== 2) . a001227) [1..]
%o A038550 -- _Reinhard Zumkeller_, May 01 2012
%o A038550 (PARI) is(n)=isprime(n>>valuation(n,2)) \\ _Charles R Greathouse IV_, Apr 30 2013
%Y A038550 Cf. A001227, A000265, A237593, A279387.
%Y A038550 Subsequences: A334101, A335431, A335911.
%Y A038550 Subsequence of A093641 and of A336101.
%K A038550 nonn,easy,nice
%O A038550 1,1
%A A038550 _Tom Verhoeff_
%E A038550 Edited by _N. J. A. Sloane_ at the suggestion of _Zak Seidov_, Sep 15 2007