A320861 Powers of 2 with initial digit 5.

512, 524288, 536870912, 549755813888, 562949953421312, 576460752303423488, 590295810358705651712, 5070602400912917605986812821504, 5192296858534827628530496329220096, 5316911983139663491615228241121378304, 5444517870735015415413993718908291383296

Offset: 1

Author

Muniru A Asiru, Oct 23 2018

Keywords

• base
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..263
• Index to divisibility sequences

Crossrefs

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

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

Programs

GAP

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

Magma

[2^n: n in [1..200] | Intseq(2^n)[#Intseq(2^n)] eq 5]; // Vincenzo Librandi, Oct 25 2018

Maple

select(x->"5"=""||x[1],[2^n$n=0..160])[];
# Alternative:
Res:= NULL: count:= 0:
for k from 1 to 49 do
   n:= ilog2(6*10^k);
   if n > ilog2(5*10^k) then count:= count+1;
     Res:= Res, 2^n;
   fi
od:
Res; # Robert Israel, Oct 26 2018

Mathematica

Select[2^Range[200], First[IntegerDigits[#]]==5 &] (* Vincenzo Librandi, Oct 25 2018 *)

PARI

lista(nn) = {for(n=1, nn, x = 2^n; if (digits(x=2^n)[1] == 5, print1(x, ", ")););} \\ Michel Marcus, Oct 25 2018