A081225 -id:A081225

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A081223

Smallest k such that floor(k*gamma) begins with n (gamma=0.5772156649...).

+10
1

2, 4, 6, 7, 9, 11, 13, 14, 16, 18, 20, 21, 23, 25, 26, 28, 30, 32, 33, 35, 37, 39, 40, 42, 44, 46, 47, 49, 51, 52, 54, 56, 58, 59, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 78, 80, 82, 84, 85, 87, 89, 91, 92, 94, 96, 98, 99, 101, 103, 104, 106, 108, 110, 111, 113, 115, 117, 118

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Based on the sequences A078219 and A078220 of Amarnath Murthy.

LINKS

Table of n, a(n) for n=1..68.

MAPLE

C := gamma; a := proc(M0, M, C) local i, d, f, g, k; description "returns the sequence 'a(n)' between 'M0' and 'M' where 'a(n)=min{k | floor(C*k) begins with n}."; d := N->`if`(N=0, [0], ListTools[Reverse](convert(N, base, 10))); f := (K, N)->`if`(d(floor(K*C))[1..min(nops(d(floor(K*C))), nops(d(N)))]=d(N), K, 0); for i from M0 to M do k := 0; while f(k, i)=0 do k := k+1; od; g(i) := f(k, i) od; return seq(g(j), j=M0..M); end proc;

CROSSREFS

Cf. A078219, A078220, A081224, A081225, A081226.

KEYWORD

nonn,base

AUTHOR

Francois Jooste (pin(AT)myway.com), Mar 10 2003

STATUS

approved

A081224

Smallest k such that floor(k*e^Pi) begins with n (e^Pi=23.14069264...).

+10
1

5, 1, 13, 2, 22, 3, 31, 35, 4, 44, 5, 52, 6, 61, 65, 7, 74, 8, 83, 9, 91, 96, 1, 104, 11, 113, 12, 121, 126, 13, 134, 14, 143, 15, 152, 156, 16, 165, 17, 173, 18, 182, 19, 191, 195, 2, 204, 21, 212, 22, 221, 225, 23, 234, 24, 242, 25, 251, 255, 26, 264, 27, 273, 28, 281

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Based on the sequences A078219 and A078220 of Amarnath Murthy.

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

a(4) = 2 because floor(2*e^Pi) = 46.

MAPLE

C := exp(Pi); a := proc(M0, M, C) local i, d, f, g, k; description "returns the sequence 'a(n)' between 'M0' and 'M' where 'a(n)=min{k | floor(C*k) begins with n}."; d := N->`if`(N=0, [0], ListTools[Reverse](convert(N, base, 10))); f := (K, N)->`if`(d(floor(K*C))[1..min(nops(d(floor(K*C))), nops(d(N)))]=d(N), K, 0); for i from M0 to M do k := 0; while f(k, i)=0 do k := k+1; od; g(i) := f(k, i) od; return seq(g(j), j=M0..M); end proc;

CROSSREFS

Cf. A078219, A078220, A081223, A081225, A081226.

KEYWORD

nonn,base

AUTHOR

Francois Jooste (pin(AT)myway.com), Mar 10 2003

STATUS

approved

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