A061581 -id:A061581 - cp's OEIS frontend

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

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

A102251 Begin with 1, multiply each digit by 2.

Original entry on oeis.org

1, 2, 4, 8, 16, 2, 12, 4, 2, 4, 8, 4, 8, 16, 8, 16, 2, 12, 16, 2, 12, 4, 2, 4, 2, 12, 4, 2, 4, 8, 4, 8, 4, 2, 4, 8, 4, 8, 16, 8, 16, 8, 4, 8, 16, 8, 16, 2, 12, 16, 2, 12, 16, 8, 16, 2, 12, 16, 2, 12, 4, 2, 4, 2, 12, 4, 2, 4, 2, 12, 16, 2, 12, 4, 2, 4, 2, 12, 4, 2, 4, 8, 4, 8, 4, 2, 4, 8, 4, 8, 4, 2, 4

Offset: 0

Alexandre Wajnberg and Eric Angelini, Feb 18 2005

Same digits as A061581 without the memory of the groupings of the preceding digits. A bunch of sequences can be produced with this rule: a(n)=d*k beginning with 1,2,3... for k=2,3,...

			Read a(5)=16 which produces a(6)=2 because 1*2=2 and a(7)=12 because 6*2=12. Now read a(6)=2 which produces [a(7) is already written] a(8)=4 because 2*2=4.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A061581.

Cf. A248131.

a102251 n = a102251_list !! n
a102251_list = 1 : (map (* 2) $
               concatMap (map (read . return) . show) a102251_list)
-- Reinhard Zumkeller, Oct 02 2014

Flatten[ NestList[ Function[x, Flatten[ FromDigits /@ 2IntegerDigits[ x]]], 1, 15]] (* Robert G. Wilson v, Feb 21 2005 *)

d*2, beginning with 1

More terms from Robert G. Wilson v, Feb 21 2005

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

A061580 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with four times its value.

Original entry on oeis.org

1, 4, 16, 424, 16816, 42432424, 1681612816816, 42432424483242432424, 168161281681616321281681612816816, 42432424483242432424424128483242432424483242432424

Offset: 1

Amarnath Murthy, May 13 2001

Michael De Vlieger, Table of n, a(n) for n = 1..16

Cf. A061581, A061582, A061583, A061584, A061585, A061586, A061587.

NestList[FromDigits@ Flatten@ Map[IntegerDigits, 4*IntegerDigits[#]] &, 1, 9] (* Michael De Vlieger, Feb 25 2023 *)

More terms from Larry Reeves (larryr(AT)acm.org) and Asher Auel, May 15 2001
a(9) corrected by N. J. A. Sloane, Jan 23 2017 at the suggestion of Carolyn Liao.
a(10) corrected by Sean A. Irvine, Feb 25 2023

A102252 Slowest increasing sequence beginning with 1 whose digits satisfy the rule d*2.

Original entry on oeis.org

1, 2, 4, 8, 16, 21, 24, 248, 481, 681, 6212, 16212, 42421, 242484, 842484, 8168168, 48168162, 121621216, 816212162, 1242421242, 4212162124, 24212424848, 42484842421, 242484842484, 816816848168, 1684842484816, 8168481681621

Offset: 1

Alexandre Wajnberg and Eric Angelini, Feb 18 2005

Same digits as A061581.

			Read a(5)=16, which produces first digit of a(6)=2 because 1*2=2 and second digit of a(6)=1 and first digit of a(7)=2 because 6*2=12.

Cf. A061581.

t = Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[2IntegerDigits[ x]]]], 1, 17]]; a = 0; l = {}; Do[k = 1; While[fd = FromDigits[ Take[t, k]]; a >= fd, k++ ]; t = Drop[t, k]; AppendTo[l, fd]; a = fd, {n, 27}]; l (* Robert G. Wilson v, Feb 21 2005 *)

d*2, beginning with 1.

More terms from Robert G. Wilson v, Feb 21 2005

A102256 Begin with 1, multiply each digit by 2, separate the digits.

Original entry on oeis.org

1, 2, 4, 8, 1, 6, 2, 1, 2, 4, 2, 4, 8, 4, 8, 1, 6, 8, 1, 6, 2, 1, 2, 1, 6, 2, 1, 2, 4, 2, 4, 2, 1, 2, 4, 2, 4, 8, 4, 8, 4, 2, 4, 8, 4, 8, 1, 6, 8, 1, 6, 8, 4, 8, 1, 6, 8, 1, 6, 2, 1, 2, 1, 6, 2, 1, 2, 1, 6, 8, 1, 6, 2, 1, 2, 1, 6, 2, 1, 2, 4, 2, 4, 2, 1, 2, 4, 2, 4, 2, 1, 2, 1, 6, 2, 1, 2, 4, 2, 4, 2, 1, 2, 4, 2

Offset: 1

Alexandre Wajnberg and Eric Angelini, Feb 19 2005

Same digits as A061581 and A102251 but separating all digits.

			Read a(4)=8 which produces, doing 8*2=16 ["1" & "6"], a(5)=1 & a(6)=6.
Now read a(5)=1 which produces [a(6) is already written] a(7)=2 because 1*2=2.
Now read a(6)=6 which produces [a(7) is already written] a(8)=1 & a(9)=2 because 6*2=12 ["1" & "2"].

Cf. A061581, A102251.

Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[ 2IntegerDigits[ x]]]], 1, 14]] (* Robert G. Wilson v, Feb 21 2005 *)

More terms from Robert G. Wilson v, Feb 21 2005

A338767 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by n.

Original entry on oeis.org

0, 1, 3, 6, 10, 65, 1211, 8988, 16171616, 1015101610151015, 11101115111011161110111511101115, 1212121112121216121212111212121712121211121212161212121112121216

Offset: 0

Jamie Robert Creasey, Nov 07 2020

This sequence is the additive counterpart of the digit factorials which, unlike the digit factorials, increases at a faster pace. A061511 and its relatives bear similarities to this sequence, but each of these increase at varying rates depending on the chosen constant. However, unlike these sequences, the constant increases by 1 each time. If digits within a(n-1) exceed 9 when one adds a constant, we ignore carrying and replace the digit with its correct value, thus 9+1 = 10. a(15) has 1024 digits.

			a(5) = {1+5, 0+5} = 65, where {x, y} is the concatenation of x and y.
a(6) = {6+6, 5+6} = 1211.

Cf. A061511-A061750, A061581-A061587, A089718, A337770.

a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(
      seq(n+l[-i], i=1..nops(l)))))(convert(a(n-1), base, 10)))
    end:
seq(a(n), n=0..12);  # Alois P. Heinz, Nov 15 2020

Nest[Append[#1, FromDigits@ Apply[Join, Map[IntegerDigits, IntegerDigits[#1[[-1]] ] + #2]]] & @@ {#, Length@ #} &, {0}, 11] (* Michael De Vlieger, Nov 13 2020 *)

cp's OEIS Frontend

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

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A102251 Begin with 1, multiply each digit by 2.

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

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A061580 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with four times its value.

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A102252 Slowest increasing sequence beginning with 1 whose digits satisfy the rule d*2.

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Mathematica

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A102256 Begin with 1, multiply each digit by 2, separate the digits.

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