A215732 a(n) is the first digit to appear n times in succession in a power of 2.

1, 5, 7, 5, 6, 8, 7, 1, 9, 9, 6, 3, 2, 9, 1, 4, 1

Offset: 1

Author

V. Raman, Aug 22 2012

Keywords

• nonn
• base
• hard
• more

Comments

Assumes that there are no 2 digits that appear n times in succession for the first time in the same power of 2. - Chai Wah Wu, Apr 26 2019

Examples

			2^16 = 65536 is the first power of 2 with a repeated digit (cf. A045875), with 5 repeated, so a(2) = 5. - _N. J. A. Sloane_, Aug 23 2012
		

Crossrefs

Cf. A045875, A215733, A215734, A215735.

Programs

Mathematica

n = 1; x = 1; lst = {};
For[i = 1, i <= 10000, i++,
z = Split[IntegerDigits[x]]; a = Length /@ z; b = Max[a];
For[j = n, j <= b, j++,
  AppendTo[lst, First[First[Part[z, First[Position[a, b]]]]]]; n++
]; x = 2 x ]; lst (* Robert Price, Mar 16 2019 *)

Python

def A215732(n):
    l, x = [str(d)*n for d in range(10)], 1
    for m in range(10**9):
        s = str(x)
        for k in range(10):
            if l[k] in s:
                return k
        x *= 2
    return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

Extensions

a(11)-a(13) added by T. D. Noe, Sep 04 2012

a(14) added by T. D. Noe, Sep 06 2012

a(15) from Bert Dobbelaere, Feb 25 2019

a(16) from Paul Geneau de Lamarlière, Jun 26 2024

a(17) from Paul Geneau de Lamarlière, Sep 24 2024