A217165
a(n) is the least value of k such that the decimal expansion of Fibonacci(k) contains n consecutive identical digits.
Original entry on oeis.org
0, 10, 49, 66, 118, 883, 2202, 6493, 62334, 135241, 353587, 1162507, 5155873, 7280413, 37356153
Offset: 1
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// See Links section.
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k = 0; Join[{0}, Table[While[d = IntegerDigits[Fibonacci[k]]; ! MemberQ[Partition[Differences[d], n - 1, 1], Table[0, {n - 1}]], k++]; k, {n, 2, 8}]] (* T. D. Noe, Oct 02 2012 *)
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def A217165(n):
if n == 1:
return 0
else:
l, y, x = [str(d)*n for d in range(10)], 0, 1
for m in range(1, 10**9):
s = str(x)
for k in l:
if k in s:
return m
y, x = x, y+x
return 'search limit reached'
# Chai Wah Wu, Dec 17 2014
A217166
a(n) is the least value of k such that the decimal expansion of Lucas(k) contains n consecutive identical digits.
Original entry on oeis.org
0, 5, 36, 78, 112, 538, 3139, 6436, 17544, 82864, 328448, 1701593, 1701593, 8030342, 8030342, 77552742
Offset: 1
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// See Links section.
-
k = 0; Join[{0}, Table[While[d = IntegerDigits[LucasL[k]]; ! MemberQ[Partition[Differences[d], n - 1, 1], Table[0, {n - 1}]], k++]; k, {n, 2, 8}]] (* T. D. Noe, Oct 02 2012 *)
-
def A217166(n):
if n == 1:
return 0
else:
l, y, x = [str(d)*n for d in range(10)], 2, 1
for m in range(1, 10**9):
s = str(x)
for k in l:
if k in s:
return m
y, x = x, y+x
return 'search limit reached'
# Chai Wah Wu, Dec 17 2014
A217186
a(n) is the number of digits in the decimal representation of the smallest power of 3 that contains n consecutive identical digits.
Original entry on oeis.org
1, 6, 16, 16, 131, 257, 1014, 3684, 10875, 51142, 51142, 304989
Offset: 1
-
k = 0; Join[{1}, Table[While[d = IntegerDigits[3^k]; prt = Partition[Differences[d], n - 1, 1]; ! MemberQ[prt, Table[0, {n - 1}]], k++]; Length[d], {n, 2, 8}]] (* T. D. Noe, Oct 03 2012 *)
-
def A217186(n):
l, x = [str(d)*n for d in range(10)], 1
for m in range(10**9):
s = str(x)
for k in l:
if k in s:
return len(s)
x *= 3
return 'search limit reached'
# Chai Wah Wu, Dec 17 2014
A238507
Smallest number m such that 3^m contains a string of n consecutive increasing integers in its decimal representation.
Original entry on oeis.org
0, 8, 20, 57, 332, 332, 6814, 7926, 16724, 200633
Offset: 1
8 is the smallest exponent such that 3^8 contains two consecutive increasing integers (3^8 = 6561).
20 is the smallest exponent such that 3^20 contains three consecutive increasing integers (3^20 = 3486784401).
A215783
The least k such that the decimal expansion of 3^k contains 9 consecutive n's.
Original entry on oeis.org
107189, 44152, 22791, 67449, 125406, 67390, 90785, 67448, 32311, 164065
Offset: 0
3^107189 = 141...2860000000000209...483 (51143 decimal digits, 0's start at position 45713).
A238508
Smallest number m such that 3^m contains a string of n consecutive decreasing integers in its decimal representation.
Original entry on oeis.org
0, 5, 13, 50, 213, 536, 536, 4582, 63202, 163984
Offset: 1
5 is the smallest exponent such that 3^5 contains two consecutive decreasing integers (3^5 = 243).
13 is the smallest exponent such that 3^13 contains three consecutive decreasing integers (3^13 = 1594323).
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