A171617 a(n)=k is the smallest exponent of N=2^k of first prime(1)=2 where at least 5 equal decimal digits "n n n n n" appear in the decimal representation of N (n=0,1,...9).

1491, 485, 314, 221, 315, 973, 220, 317, 316, 422

Offset: 0

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 13 2009

Keywords

• nonn
• base
• fini
• full

Comments

If we change the definition to allow for not just the digits but for the numbers, say "10" then this sequence can be extended. a(10) would become 263528 and a(11) would equal 165742. - Robert G. Wilson v, Oct 13 2012

Examples

			0: 2^1491: 449 decimal digits, "00000" appears on decimals 397 - 401.
1: 2^485: 146 decimal digits, "11111" appears on decimals 22 - 26.
2: 2^314: 95 decimal digits, "22222" appears on decimals 64 - 68.
3: 2^221: 67 decimal digits, "33333" appears on decimals 7 - 11.
4: 2^315: 95 decimal digits, "44444" appears on decimals 64 - 68.
5: 2^973: 293 decimal digits, "555555" (6 "5's") appears on decimals 230 - 25.
6: 2^220: 67 decimal digits, "66666" appears on decimals 7 - 11.
7: 2^317: 96 decimal digits, "77777" appears on decimals 65 - 69.
8: 2^316: 96 decimal digits, "88888" appears on decimals 65 - 69.
9: 2^422: 128 decimal digits, "99999" appears on decimals 83 - 87.
		

References

• E. J. Burr, American Mathematical Monthly (December 1963, 70(10), pp. 1101-2
• Julian Havil, Impossible?: Surprising Solutions to Counterintuitive Conundrums, Princeton University Press 2008
• Ross Honsberger, Ingenuity in mathematics, Random House/Singer School Division 1970

Crossrefs

Cf. A000079, A018802, A171132, A171242, A171489.

Programs

Mathematica

f[n_] := Block[{k = 1, m = IntegerString[n]}, mm = m <> m <> m <> m <> m; While[ StringPosition[ ToString[2^k], mm] == {}, k++]; k]; Array[f, 10, 0] (* Robert G. Wilson v, Oct 13 2012 *)