A141839 -id:A141839 - cp's OEIS frontend

A141836 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 2 so that each interpretation is base 3. Terms already fully reduced (i.e., single digits) are excluded.

12, 202, 21111, 1001221220, 2120202222022022102

Offset: 1

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008

It is possible to compute additional terms by taking the last term, treating it as base-10 and converting to base-3. This will necessarily create a term which can converted back to base 10 yielding the previous term in the sequence which will itself yield N further terms. But there is no guarantee (except in base 2) that the term so derived will be the first term to produce a sequence of N+1 terms. There could be another, smaller, term which satisfies that requirement but which uses different terms. Pushing the last term of this sequence yields 2120202222022022102 as a possible next term.

			a(3) = 21111 because 21111 is the first number that can produce a sequence of three terms by repeated interpretation as a base 3 number: [21111] (base-3) --> [202] (base-3) --> [20] (base-3) --> [6]. Since 6 cannot be interpreted as a base 3 number, the sequence terminates with 20. a(1) = 12 because 12 is the first number that can be reduced once, yielding no further terms interpretable as base 3.

Cf. A091049, A141837, A141838, A141839, A141840, A141841, A141842.

a(5) from Giovanni Resta, Feb 23 2013

A141837 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 3 so that each interpretation is base 4. Terms already fully reduced (i.e., single digits) are excluded.

Original entry on oeis.org

13, 31, 133, 120332323, 13023002000203

Offset: 1

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008

It is possible to compute additional terms by taking the last term, treating it as base-10 and converting to base-4. This will necessarily create a term which can converted back to base 10 yielding the previous term in the sequence which will itself yield N further terms. But there is no guarantee (except in base 2) that the term so derived will be the first term to produce a sequence of N+1 terms. There could be another, smaller, term which satisfies that requirement but which uses different terms. Pushing the last term of this sequence yields 13023002000203 as a possible next term.

			a(3) = 133 because 133 is the first number that can produce a sequence of three terms by repeated interpretation as a base 4 number: [133] (base-4) --> [31] (base-4) --> [13] (base-4) --> [7]. Since 7 cannot be interpreted as a base 4 number, the sequence terminates with 13. a(1) = 13 because 13 is the first number that can be reduced once, yielding no further terms interpretable as base 4.

Cf. A091049, A141836, A141838, A141839, A141840, A141841, A141842.

a(5) from Giovanni Resta, Feb 23 2013

A141838 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 4 so that each interpretation is base 5. Terms already fully reduced (i.e., single digits) are excluded.

Original entry on oeis.org

14, 24, 44, 134, 1014, 13024, 404044, 100412134, 201201142014

Offset: 1

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008

It is possible to compute additional terms by taking the last term, treating it as base-10 and converting to base-5. This will necessarily create a term which can converted back to base 10 yielding the previous term in the sequence which will itself yield N further terms. But there is no guarantee (except in base 2) that the term so derived will be the first term to produce a sequence of N+1 terms. There could be another, smaller, term which satisfies that requirement but which uses different terms. Pushing the last term of this sequence yields 201201142014 as a possible next term.

			a(3) = 44 because 44 is the first number that can produce a sequence of three terms by repeated interpretation as a base 5 number: [44] (base-5) --> [24] (base-5) --> [14] (base-5) --> [9]. Since 9 cannot be interpreted as a base 5 number, the sequence terminates with 14. a(1) = 14 because 14 is the first number that can be reduced once, yielding no further terms interpretable as base 5.

Cf. A091049, A141836, A141837, A141839, A141840, A141841, A141842.

a(9) from Giovanni Resta, Feb 23 2013

A141840 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 6 so that each interpretation is base 7. Terms already fully reduced (i.e., single digits) are excluded.

Original entry on oeis.org

16, 64, 631, 1561, 4360, 15466, 63043, 34406005, 565306024, 23001126626004, 4562530234315632

Offset: 1

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008

It is sometimes possible to compute additional terms by taking the last term, treating it as base 10 and converting to base 7. This may create a term minimally interpretable as base 7 which can converted back to base 10 yielding the previous term in the sequence which will itself yield N further terms. But there is no guarantee (except in base 2) that the term so derived will be the first term to produce a sequence of N+1 terms. There could be another, smaller, term which satisfies that requirement but which uses different terms. Pushing the last term of this sequence does not produce a value minimally interpretable as base 7.

			a(3) = 631 because 631 is the first number that can produce a sequence of three terms by repeated interpretation as a base 7 number: [631] (base-7) --> [316] (base-7) --> [160] (base-7) --> [91]. Since 91 cannot be minimally interpreted as a base 7 number, the sequence terminates with 160. a(1) = 16 because 16 is the first number that can be reduced once, yielding no further terms minimally interpretable as base 7.

Cf. A091049, A141836, A141837, A141838, A141839, A141841, A141842.

a(10)-a(11) from Giovanni Resta, Feb 23 2013

A141841 a(n) is the first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 7 so that each interpretation is base 8. Terms already fully reduced (i.e., single digits) are excluded.

Original entry on oeis.org

17, 57, 71, 107, 4647, 11047, 25447, 61547, 170153, 115751335, 671434647, 5001243627, 45206165753

Offset: 1

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008

It is sometimes possible to compute additional terms by taking the last term, treating it as base 10 and converting to base 8. This may create a term minimally interpretable as base 8 which can converted back to base 10 yielding the previous term in the sequence which will itself yield N further terms. But there is no guarantee (except in base 2) that the term so derived will be the first term to produce a sequence of N+1 terms. There could be another, smaller, term which satisfies that requirement but which uses different terms. Pushing the last term of this sequence produces the value 5001243627 which is minimally interpretable as base 8.

			a(3) = 71 because 71 is the first number that can produce a sequence of three terms by repeated interpretation as a base 8 number: [71] (base-8) --> [57] (base-8) --> [47] (base-8) --> [39]. Since 39 cannot be minimally interpreted as a base 8 number, the sequence terminates with 47. a(1) = 17 because 17 is the first number that can be reduced once, yielding no further terms minimally interpretable as base 8.

Cf. A091049, A141836, A141837, A141838, A141839, A141840, A141842.

a(12)-a(13) from Giovanni Resta, Feb 23 2013

A141842 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 8 so that each interpretation is base 9. Terms already fully reduced (i.e., single digits) are excluded.

Original entry on oeis.org

18, 86, 680, 835, 7087, 12788, 18478, 128117, 385732, 2206280, 13176873, 33185141, 68388408, 335213686, 1365888758, 4771043885, 24740884085

Offset: 1

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008

It is sometimes possible to compute additional terms by taking the last term, treating it as base 10 and converting to base 9. This may create a term minimally interpretable as base 9 which can converted back to base 10 yielding the previous term in the sequence which will itself yield N further terms. But there is no guarantee (except in base 2) that the term so derived will be the first term to produce a sequence of N+1 terms. There could be another, smaller, term which satisfies that requirement but which uses different terms. Pushing a(15) does not produce a value minimally interpretable as base 9.

			a(3) = 680 because 680 is the first number that can produce a sequence of three terms by repeated interpretation as a base 9 number: [680] (base-9) --> [558] (base-9) --> [458] (base-9) --> [377]. Since 377 cannot be minimally interpreted as a base 9 number, the sequence terminates with 458. a(1) = 18 because 18 is the first number that can be reduced once, yielding no further terms minimally interpretable as base 9.

Cf. A091049, A141836, A141837, A141838, A141839, A141840, A141841.

a(16)-a(17) from Giovanni Resta, Feb 23 2013

cp's OEIS Frontend

A141836 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 2 so that each interpretation is base 3. Terms already fully reduced (i.e., single digits) are excluded.

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A141837 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 3 so that each interpretation is base 4. Terms already fully reduced (i.e., single digits) are excluded.

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A141838 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 4 so that each interpretation is base 5. Terms already fully reduced (i.e., single digits) are excluded.

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A141840 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 6 so that each interpretation is base 7. Terms already fully reduced (i.e., single digits) are excluded.

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A141841 a(n) is the first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 7 so that each interpretation is base 8. Terms already fully reduced (i.e., single digits) are excluded.

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A141842 a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 8 so that each interpretation is base 9. Terms already fully reduced (i.e., single digits) are excluded.

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