cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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

Views

Author

Amarnath Murthy, May 08 2001

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

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

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

Views

Author

Amarnath Murthy, May 08 2001

Keywords

Comments

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

Links

Crossrefs

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

Programs

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

Extensions

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

Views

Author

Amarnath Murthy, May 08 2001

Keywords

Comments

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

Links

Crossrefs

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

Programs

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

Extensions

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

Views

Author

Amarnath Murthy, May 08 2001

Keywords

Comments

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

Examples

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

Crossrefs

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

Programs

  • Mathematica
    NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+2)]]&,0,30] (* Harvey P. Dale, Jul 07 2012 *)
  • PARI
    A061513(n)=10^2^(n\5)\9*(n%5*2+1)-1 \\ M. F. Hasler, Jun 24 2016

Formula

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

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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