A061587 -id:A061587 - 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

A061581 a(1) = 1, a(n) = number obtained by replacing each digit of a(n-1) with its double.

Original entry on oeis.org

1, 2, 4, 8, 16, 212, 424, 848, 16816, 21216212, 424212424, 848424848, 1681684816816, 212162121681621216212, 42421242421216212424212424, 848424848424212424848424848, 16816848168168484248481681684816816

Offset: 1

Amarnath Murthy, May 13 2001

It might have been more natural to start with index / offset 0. - M. F. Hasler, Jun 24 2016

			The term after 16 is 2.12, i.e., 212.

Alois P. Heinz, Table of n, a(n) for n = 1..29

Cf. A061582 - A061587.

a:= proc(n) option remember; `if`(n=1, 1, (l->
       parse(cat(seq(2*l[-i], i=1..nops(l)))))(
             convert(a(n-1), base, 10)))
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Jun 24 2016

NestList[FromDigits[Flatten[IntegerDigits[2*IntegerDigits[#]]]] &,1,16] (* Jayanta Basu, May 20 2013 *)

A061581(n=2,a=1,m=2)={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

A061750 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 9.

Original entry on oeis.org

0, 9, 18, 1017, 1091016, 109181091015, 109181017109181091014, 1091810171091016109181017109181091013, 10918101710910161091810910151091810171091016109181017109181091012

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 sequence converges to the limit 109181017109101610918109..... - M. F. Hasler, Jun 24 2016
a(13) has 1078 decimal digits. - Michael De Vlieger, Jun 24 2016

Michael De Vlieger, Table of n, a(n) for n = 0..12

Cf. A061511 - A061522, A061746 - A061749; A061581 - A061587.

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

A061750(n=2, a=9, m=9)={for(n=2,n, a=eval(concat(apply(t->Str(t+m), digits(a)))));if(n,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

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

A061582 a(1) = 1, a(n) = number obtained by replacing each digit of a(n-1) with three times its value.

Original entry on oeis.org

1, 3, 9, 27, 621, 1863, 324189, 961232427, 2718369612621, 6213249182718361863, 1863961227324621324918324189, 32418927183662196121863961227324961232427, 961232427621324918186327183632418927183662196122718369612621

Offset: 1

Amarnath Murthy, May 13 2001

Number of digits of each term in this sequence is sequence A000930. - Dmitry Kamenetsky, Jan 17 2009
Each of the subsequences a(5n), a(5n-1), ..., a(5n-4) seem to converge to a different fixed point of the operation (if the terms are seen as sequences of digits). - M. F. Hasler, Jun 24 2016
a(20) has 1278 decimal digits. - Michael De Vlieger, Jun 24 2016

Michael De Vlieger, Table of n, a(n) for n = 1..20

Cf. A061581 - A061587.

NestList[FromDigits@ Flatten@ Map[IntegerDigits, 3 IntegerDigits@ #] &, 1, 12] (* Michael De Vlieger, Jun 24 2016 *)

A061582(n=2,a=1,m=3)={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), May 14 2001

A061586 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with eight times its value.

Original entry on oeis.org

1, 8, 64, 4832, 32642416, 241648321632848, 1632848326424168482416643264, 84824166432642416483216328486432641632848483224164832, 64326416328484832241648321632848326424168482416643264483224164832848241664326432642416163284832642416

Offset: 1

Amarnath Murthy, May 13 2001

John Cerkan, Table of n, a(n) for n = 1..12

Cf. A061581-A061587.

NestList[FromDigits[Flatten[IntegerDigits/@(8*IntegerDigits[#])]]&,1,10] (* Harvey P. Dale, Sep 22 2012 *)

def A061586_first(n):
    an = "1"
    cnt = 1
    a061586 = []
    while cnt < n:
        a061586.append(int(an))
        newan = ""
        for i in an:
            newan += str(8*int(i))
        an = newan
        cnt += 1
    a061586.append(int(an))
    return a061586 # John Cerkan, May 25 2018

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

A061583 a(1) = 1, a(n) is the number obtained by replacing each digit of a(n-1) with five times its value.

Original entry on oeis.org

1, 5, 25, 1025, 501025, 250501025, 10250250501025, 501025010250250501025, 2505010250501025010250250501025, 1025025050102502505010250501025010250250501025

Offset: 1

Amarnath Murthy, May 13 2001

Number of digits of each term is the sequence A038718. - Dmitry Kamenetsky, Jan 17 2009

John Cerkan, Table of n, a(n) for n = 1..17

Cf. A061581, A061582, A061584, A061585, A061586, A061587.

a:= proc(n) option remember; `if`(n=1, 1, (s-> parse(cat(
      seq(parse(s[i])*5, i=1..length(s)))))(""||(a(n-1))))
    end:
seq(a(n), n=1..10);  # Alois P. Heinz, May 25 2018

NestList[FromDigits[Flatten[IntegerDigits/@(5*IntegerDigits[#])]]&,1,10] (* Harvey P. Dale, Dec 31 2013 *)

def A061583_first(n):
    an = "1"
    a061583 = []
    while n > 1:
        a061583.append(int(an))
        newan = ""
        for i in an:
            newan += str(5*int(i))
        an = newan
        n -= 1
    a061583.append(int(an))
    return a061583 # John Cerkan, May 25 2018

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

A061584 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with six times its value.

Original entry on oeis.org

1, 6, 36, 1836, 6481836, 3624486481836, 1836122424483624486481836, 64818366121224122424481836122424483624486481836, 362448648183636612612122461212241224244864818366121224122424481836122424483624486481836

Offset: 1

Amarnath Murthy, May 13 2001

a(n) contains all of a(n-1) as its least significant digits.

John Cerkan, Table of n, a(n) for n = 1..13

Cf. A061581, A061582, A061583, A061585, A061586, A061587, A061533.

NestList[FromDigits[Flatten[IntegerDigits/@(6 IntegerDigits[#])]]&,1,10] (* Harvey P. Dale, Aug 26 2022 *)

def A061584_first(n):
    an = "1"
    a061584 = []
    while n > 1:
        a061584.append(int(an))
        newan = ""
        for i in an:
            newan += str(6*int(i))
        an = newan
        n -= 1
    a061584.append(int(an))
    return a061584 # John Cerkan, May 25 2018

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

A061585 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with seven times its value.

Original entry on oeis.org

1, 7, 49, 2863, 14564221, 72835422814147, 49145621352814145672872849, 286372835421472135145672872835424914564914562863, 1456422149145621352814728491472135728354249145649145621352814286372835422863728354214564221

Offset: 1

Amarnath Murthy, May 13 2001

John Cerkan, Table of n, a(n) for n = 1..12

Cf. A061581, A061582, A061583, A061584, A061586, A061587.

NestList[FromDigits[Flatten[IntegerDigits/@(7*IntegerDigits[#])]]&,1,10] (* Harvey P. Dale, Jan 23 2015 *)

A061585(n=2,a=1,m=7)={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

def A061585_first(n):
    an = "1"
    a061585 = []
    while n > 1:
        a061585.append(int(an))
        newan = ""
        for i in an:
            newan += str(7*int(i))
        an = newan
        n -= 1
    a061585.append(int(an))
    return a061585 # John Cerkan, May 25 2018

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

Corrected by Harvey P. Dale, Jan 23 2015

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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A061581 a(1) = 1, a(n) = number obtained by replacing each digit of a(n-1) with its double.

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A061750 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 9.

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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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A061582 a(1) = 1, a(n) = number obtained by replacing each digit of a(n-1) with three times its value.

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A061586 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with eight 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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