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A215511 A sequence of prime numbers expressed as minimum bases using only digits 0 and 1. 1
10, 10, 11, 101, 111, 1011, 10001, 10011, 11101, 11111, 11101, 10011, 10111, 101111 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
COMMENTS
3 = 10 base 3 = 3 + 0
5 = 10 base 5 = 5 + 0
7 = 11 base 6 = 6 + 1
37 = 101 base 6 = 36 + 0 + 1
43 = 111 base 6 = 36 + 6 + 1
223 = 1011 base 6 = 216 + 0 + 6 + 1
1297 = 10001 base 6 = 1296 + 0 + 0 + 0 + 1
1303 = 10011 base 6 = 1296 + 0 + 0 + 6 + 1
1549 = 11101 base 6 = 1296 + 216 + 36 + 0 + 1
2801 = 11111 base 7 = 2401 + 343 + 49 + 7 + 1
4673 = 11101 base 8 = 4096 + 512 + 64 + 0 + 1
6571 = 10011 base 9 = 6561 + 0 + 0 + 9 + 1
10111 = 10111 base 10 = 10000 + 0 + 100 + 10 + 1
101111 = 101111 base 10 = 100000 + 0 + 1000 + 100 + 10 + 1
LINKS
FORMULA
Step 1: Starting at the first prime number (3), convert to the minimum base (3, as all primes may be expressed in binary).
Step 2: If the next prime number can be converted into the same base using only 0 and 1 without exceeding the value of the next prime number in the next base, this is the next item in the sequence.
Step 3: If the next prime number cannot be expressed in this base before exceeding the value of the next prime number in the next base, skip this prime number and move on to the next prime number and repeat Step 2.
Step 4: If the next prime number cannot be expressed in this base before exceeding the value of the next prime number in the next base, but can be expressed in the next base, this is the next item in the sequence.
EXAMPLE
The first term is 3 in base 3. The next prime in that base is 13, which is greater than the value of the prime in the next base, which is 5 in base 4, so the second term is 5 in base 4.
CROSSREFS
Sequence in context: A004209 A162720 A112867 * A280105 A173198 A111381
KEYWORD
nonn,base
AUTHOR
Jason Betts, Aug 14 2012.
STATUS
approved

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Last modified February 21 02:19 EST 2024. Contains 370219 sequences. (Running on oeis4.)