A067490 Powers of 4 with initial digit 1.

1, 16, 1024, 16384, 1048576, 16777216, 1073741824, 17179869184, 1099511627776, 17592186044416, 1125899906842624, 18014398509481984, 1152921504606846976, 18446744073709551616, 1180591620717411303424, 18889465931478580854784, 1208925819614629174706176

Offset: 1

Author

Amarnath Murthy, Feb 09 2002

Keywords

• base
• easy
• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..400
• Index to divisibility sequences

Crossrefs

Cf. A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A067488, A067489.

Programs

GAP

Filtered(List([0..40],n->4^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018

Maple

select(x-> "1"=""||x[1],[4^n$n=0..60])[];  # Alois P. Heinz, Oct 22 2018

Formula

a(n+1)/a(n) is in {16, 64, 1024}, so 16^n <= a(n+1) < 1024^n. Asymptotically, the exponent should be 100; I can prove that 99^n << a(n) << 101^n. [Charles R Greathouse IV, Jan 19 2012]

Extensions

a(16) inserted by Muniru A Asiru, Oct 22 2018