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Powers of 2 with initial digit 5.
5

%I #18 Sep 08 2022 08:46:23

%S 512,524288,536870912,549755813888,562949953421312,576460752303423488,

%T 590295810358705651712,5070602400912917605986812821504,

%U 5192296858534827628530496329220096,5316911983139663491615228241121378304,5444517870735015415413993718908291383296

%N Powers of 2 with initial digit 5.

%H Robert Israel, <a href="/A320861/b320861.txt">Table of n, a(n) for n = 1..263</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

%p select(x->"5"=""||x[1],[2^n$n=0..160])[];

%p # Alternative:

%p Res:= NULL: count:= 0:

%p for k from 1 to 49 do

%p n:= ilog2(6*10^k);

%p if n > ilog2(5*10^k) then count:= count+1;

%p Res:= Res, 2^n;

%p fi

%p od:

%p Res; # _Robert Israel_, Oct 26 2018

%t Select[2^Range[200], First[IntegerDigits[#]]==5 &] (* _Vincenzo Librandi_, Oct 25 2018 *)

%o (GAP) Filtered(List([0..160],n->2^n),i->ListOfDigits(i)[1]=5);

%o (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 (Magma) [2^n: n in [1..200] | Intseq(2^n)[#Intseq(2^n)] eq 5]; // _Vincenzo Librandi_, Oct 25 2018

%Y Cf. A000079 (powers of 2), A008952 (leading digit of 2^n).

%Y Powers of 2 with initial digit k, (k = 1..5): A067488, A067480, A320859, A320860, this sequence.

%K base,nonn

%O 1,1

%A _Muniru A Asiru_, Oct 23 2018