A061750 -id:A061750 - cp's OEIS frontend

A061511 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 1.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 2110, 3221, 4332, 5443, 6554, 7665, 8776, 9887, 10998, 2110109, 32212110, 43323221, 54434332, 65545443, 76656554, 87767665, 98878776, 109989887, 211010910998

Offset: 0

Amarnath Murthy, May 08 2001

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.
a(n+10) is the concatenation of a(n) and a(n-1).
Considering each term as a sequence of digits, each of the subsequences a(9n), a(9n-1), ... and a(9n-8) converges to a different limit. - M. F. Hasler, Jun 24 2016

			Following 43: 4+1 = 5 and 3+1 = 4, hence the next term is 54.

Indranil Ghosh, Table of n, a(n) for n = 0..97

Cf. A061512 - A061522, A061746 - A061750; A061581 - A061587.

NestList[FromDigits[Flatten[IntegerDigits[IntegerDigits[#]+1]]]&,0,38] (* Jayanta Basu, May 18 2013 *)

A061511(n=2, a=n>0, m=1)={for(n=2, n, a=eval(concat(apply(t->Str(t+m), digits(a))))); a} \\ If only the 2nd argument is given, then the operation is applied once to that argument. - M. F. Hasler, Jun 24 2016

A061522 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 7.

Original entry on oeis.org

0, 7, 14, 811, 1588, 8121515, 1589812812, 812151615891589, 158981281381215168121516, 812151615891581015898128131589812813, 15898128138121516812158781215161589158108121516158915810

Offset: 0

Amarnath Murthy, May 08 2001

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.

			In the sequence 1588 follows 811 because 8+7 = 15 and 1+7 = 8. - _Indranil Ghosh_, Feb 09 2017

Indranil Ghosh, Table of n, a(n) for n = 0..16

NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+7)]]&,0,10] (* Harvey P. Dale, Jun 05 2023 *)

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061746 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 7.

Original entry on oeis.org

1, 8, 15, 812, 1589, 8121516, 1589812813, 8121516158915810, 158981281381215168121587, 8121516158915810158981281315898121514, 158981281381215168121587812151615891581081215161589812811

Offset: 0

Amarnath Murthy, May 08 2001

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.

Considering each term as a sequence of digits, the subsequences a(2n) and a(2n-1) converge to two different fixed points of the operation repeated twice, 158981281381... and 81215161589158.... - M. F. Hasler, Jun 24 2016

Harvey P. Dale, Table of n, a(n) for n = 0..16

Cf. A061747 - A061750, A061511 - A061522; A061581 - A061587.

NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+7)]]&,1,10] (* Harvey P. Dale, Jun 07 2025 *)

A061746(n=1, a=1, m=7)={for(n=1, n, a=eval(concat(apply(t->Str(t+m), digits(a))))); a} \\ If only the 2nd argument is given, then the operation is applied once to that argument. - M. F. Hasler, Jun 24 2016

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061587 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with nine times its value.

Original entry on oeis.org

1, 9, 81, 729, 631881, 5427972729, 45361863816318631881, 36452754972542772954279725427972729, 2754364518634536816318453618636318814536186381631845361863816318631881

Offset: 1

Amarnath Murthy, May 13 2001

Each of the subsequences a(9n), a(9n-1), ..., and a(9n-8) converges to a different limit, if we consider the numbers as sequences of digits. - M. F. Hasler, Jun 24 2016

Indranil Ghosh, Table of n, a(n) for n = 1..13

Cf. A061581 - A061586, A061511-A061522, A061746-A061750.

A061587(n=2,a=1,m=9)={while(n--,a=eval(concat(apply(t->Str(t),digits(a)*m))));a} \\ If only the 2nd argument is given, then the operation is applied once to that argument. - M. F. Hasler, Jun 24 2016

More terms from Larry Reeves (larryr(AT)acm.org) and Asher Auel, May 15 2001

A061512 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 2.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 33, 55, 77, 99, 1111, 3333, 5555, 7777, 9999, 11111111, 33333333, 55555555, 77777777, 99999999, 1111111111111111, 3333333333333333, 5555555555555555, 7777777777777777, 9999999999999999, 11111111111111111111111111111111, 33333333333333333333333333333333

Offset: 0

Amarnath Murthy, May 08 2001

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.

Also: odd repdigits (A010785) of length 2^k, cf. formula. - M. F. Hasler, Jun 24 2016

			Following 33: 3+2 = 5 and 3+2 = 5, hence the next term is 55.

Cf. A061511 - A061522, A061746 - A061750; A061581 - A061587.

Cf. also A010785.

NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+2)]]&,1,30] (* Harvey P. Dale, Apr 13 2012 *)

A061512(n)=10^2^(n\5)\9*(n%5*2+1) \\ M. F. Hasler, Jun 24 2016

nxt(n) = my(d=digits(n)); if(d[1]<9,n+2*(10^#d - 1)/9,(10^(2*#d) - 1)/9)
inv(n) = {my(d=digits(n));5*logint(#d,2) + (d[1]+1)\2} \\ David A. Corneth, Jun 24 2016

a(n) = (10^2^floor(n/5)-1)/9*(n%5*2+1), where n%5 means the remainder (in {0..4}) of n divided by 5. - M. F. Hasler, Jun 24 2016

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061519 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 5.

Original entry on oeis.org

1, 6, 11, 66, 1111, 6666, 11111111, 66666666, 1111111111111111, 6666666666666666, 11111111111111111111111111111111, 66666666666666666666666666666666

Offset: 0

Amarnath Murthy, May 08 2001

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.

Number of digits of each term is the sequence A016116. [From Dmitry Kamenetsky, Jan 17 2009]

Harvey P. Dale, Table of n, a(n) for n = 0..13

With[{nn=5},Join[Table[FromDigits[PadRight[{},2^n,1]],{n,0,nn}],Table[FromDigits[PadRight[{},2^n,6]],{n,0,nn}]]]//Sort (* Harvey P. Dale, Jan 23 2025 *)

a(2n) = 6*[10^{2^(n)} - 1]/9 a(2n+1) = [10^(2^n) - 1]/9

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061747 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 8.

Original entry on oeis.org

0, 8, 16, 914, 17912, 91517910, 179139151798, 91517911179139151716, 1791391517999151791117913915914, 91517911179139151717179139151799915179111791317912

Offset: 0

Amarnath Murthy, May 08 2001

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.
Considering each term as a sequence of digits, the subsequences a(2n) and a(2n-1) converge to two different fixed points of the operation, 17913915179... and 915179111791391517.... More precisely, the digits of a(n) except the last are the first digits of a(n+2). - M. F. Hasler, Jun 24 2016
a(16) has 1270 decimal digits. - Michael De Vlieger, Jun 24 2016

Michael De Vlieger, Table of n, a(n) for n = 0..15

Cf. A061746 - A061750, A061511 - A061522; A061581 - A061587.

NestList[FromDigits@ Flatten@ Map[IntegerDigits, IntegerDigits[#] + 8] &, 0, 9] (* Michael De Vlieger, Jun 24 2016, after Harvey P. Dale at A061512 *)

A061747(n=2, a=if(n,8), m=8)={for(n=2, n, a=eval(concat(apply(t->Str(t+m), digits(a))))); a} \\ If only the 2nd argument is given, then the operation is applied once to that argument. - M. F. Hasler, Jun 24 2016

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061749 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 9.

Original entry on oeis.org

1, 10, 109, 10918, 109181017, 1091810171091016, 1091810171091016109181091015, 1091810171091016109181091015109181017109181091014

Offset: 0

Amarnath Murthy, May 08 2001

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.

Considering each term as a sequence of digits, this sequence converges to the same limit as A061750, 109181017109101610918109..., fixed point of the operation. - M. F. Hasler, Jun 24 2016

Cf. A061746 - A061750, A061511 - A061522; A061581 - A061587.

A061749(n=1, a=1, m=9)={for(n=1, n, a=eval(concat(apply(t->Str(t+m), digits(a))))); a} \\ If only the 2nd argument is given, then the operation is applied once to that argument. - M. F. Hasler, Jun 24 2016

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061513 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 2.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 32, 54, 76, 98, 1110, 3332, 5554, 7776, 9998, 11111110, 33333332, 55555554, 77777776, 99999998, 1111111111111110, 3333333333333332, 5555555555555554, 7777777777777776, 9999999999999998, 11111111111111111111111111111110, 33333333333333333333333333333332

Offset: 0

Amarnath Murthy, May 08 2001

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.
Every term > 8 is made up of only two different consecutive digits, the smaller of which occurs only as the least significant digit.
Otherwise said, these are one less than the odd repdigits (A010785) of length 2^k, cf. formula. - M. F. Hasler, Jun 24 2016

			Following 32; 3+2 = 5 and 2+2 = 4, hence the next term is 54.

Cf. A061511 - A061522, A061746 - A061750; A061581 - A061587.

NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+2)]]&,0,30] (* Harvey P. Dale, Jul 07 2012 *)

A061513(n)=10^2^(n\5)\9*(n%5*2+1)-1 \\ M. F. Hasler, Jun 24 2016

a(n) = A061512(n)-1 = (10^2^floor(n/5)-1)/9*(n%5*2+1) - 1, where n%5 means the remainder (in {0..4}) of n divided by 5. - M. F. Hasler, Jun 24 2016

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061517 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 4.

Original entry on oeis.org

0, 4, 8, 12, 56, 910, 1354, 5798, 9111312, 13555756, 5799911910, 911131313551354, 1355575757995798, 579991191191113139111312, 9111313135513551355575713555756, 135557575799579957999119115799911910

Offset: 0

Amarnath Murthy, May 08 2001

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.

Harvey P. Dale, Table of n, a(n) for n = 0..27

NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+4)]]&,0,20] (* Harvey P. Dale, Nov 20 2020 *)

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

cp's OEIS Frontend

A061511 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 1.

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A061522 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 7.

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A061746 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 7.

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A061587 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with nine times its value.

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A061512 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 2.

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A061519 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 5.

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A061747 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 8.

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A061749 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 9.

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