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A320861 Powers of 2 with initial digit 5.

%I A320861 #18 Sep 08 2022 08:46:23
%S A320861 512,524288,536870912,549755813888,562949953421312,576460752303423488,
%T A320861 590295810358705651712,5070602400912917605986812821504,
%U A320861 5192296858534827628530496329220096,5316911983139663491615228241121378304,5444517870735015415413993718908291383296
%N A320861 Powers of 2 with initial digit 5.
%H A320861 Robert Israel, <a href="/A320861/b320861.txt">Table of n, a(n) for n = 1..263</a>
%H A320861 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%p A320861 select(x->"5"=""||x[1],[2^n$n=0..160])[];
%p A320861 # Alternative:
%p A320861 Res:= NULL: count:= 0:
%p A320861 for k from 1 to 49 do
%p A320861    n:= ilog2(6*10^k);
%p A320861    if n > ilog2(5*10^k) then count:= count+1;
%p A320861      Res:= Res, 2^n;
%p A320861    fi
%p A320861 od:
%p A320861 Res; # _Robert Israel_, Oct 26 2018
%t A320861 Select[2^Range[200], First[IntegerDigits[#]]==5 &] (* _Vincenzo Librandi_, Oct 25 2018 *)
%o A320861 (GAP) Filtered(List([0..160],n->2^n),i->ListOfDigits(i)[1]=5);
%o A320861 (PARI) lista(nn) = {for(n=1, nn, x = 2^n; if (digits(x=2^n)[1] == 5, print1(x, ", ")););} \\ _Michel Marcus_, Oct 25 2018
%o A320861 (Magma) [2^n: n in [1..200] | Intseq(2^n)[#Intseq(2^n)] eq 5]; // _Vincenzo Librandi_, Oct 25 2018
%Y A320861 Cf. A000079 (powers of 2), A008952 (leading digit of 2^n).
%Y A320861 Powers of 2 with initial digit k, (k = 1..5): A067488, A067480, A320859, A320860, this sequence.
%K A320861 base,nonn
%O A320861 1,1
%A A320861 _Muniru A Asiru_, Oct 23 2018