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 1-3 of 3 results.

A318275 Numbers with digits in nondecreasing order and with multiplicative digital root > 0.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 46, 47, 48, 49, 57, 66, 67, 68, 77, 79, 88, 89, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 126, 127, 128, 129, 133, 134
Offset: 1

Views

Author

David A. Corneth, Aug 23 2018

Keywords

Comments

This sequence is a primitive sequence of A277061, it has digits in nondecreasing order. Terms in A277061 can be found by permuting digits of terms of this sequence.

Crossrefs

Cf. A009994, A277061, A299690.

Programs

  • Mathematica
    Select[Range@ 134, And[FixedPoint[Times @@ IntegerDigits@ # &, #] != 0, AllTrue[Differences@ IntegerDigits@ #, # >= 0 &]] &] (* Michael De Vlieger, Aug 25 2018 *)

A318276 Numbers with digits in nondecreasing order without digit 1 whose multiplicative digital root is not 0.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 24, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 46, 47, 48, 49, 57, 66, 67, 68, 77, 79, 88, 89, 99, 222, 223, 224, 226, 227, 228, 229, 233, 234, 236, 237, 238, 244, 246, 248, 249, 266, 267, 277, 278, 279, 288, 289, 299, 333, 334
Offset: 1

Views

Author

David A. Corneth, Aug 23 2018

Keywords

Comments

This sequence is a primitive sequence of A299690 because terms of that sequence can be found using this; permuting digits of terms of this sequence gives terms in A299690.
This sequence is also a primitive sequence to A318275 as prepending 0 or more ones to terms in this sequence gives terms in A318275.
This sequence is finite because it's a subsequence of the finite sequence A299690.

Links

Crossrefs

Cf. A299690, A318275.

Programs

  • Mathematica
    Select[Range[333], And[FreeQ[IntegerDigits@ #, 1], FixedPoint[Times @@ IntegerDigits@ # &, #] != 0, AllTrue[Differences@ IntegerDigits@ #, # >= 0 &]] &] (* Michael De Vlieger, Aug 25 2018 *)
  • PARI
    mdr(n)=n = fromdigits(n); while(n>9, n=factorback(digits(n))); n \\ from Charles R Greathouse IV at A299690.
uptoQdigits(n) = {my(res = List()); for(i = 1, n, forvec(x = vector(i, j, [2, 9]), c = mdr(x); if(c != 0, listput(res, fromdigits(x))), 1)); res} \\ David A. Corneth, Dec 31 2018

Extensions

Data corrected by David A. Corneth, Dec 31 2018

A318273 Numbers with digits in nondecreasing order such that additive and multiplicative digital roots coincide.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 123, 137, 139, 168, 179, 188, 233, 267, 299, 346, 389, 899, 1124, 1157, 1347, 1355, 1469, 1779, 1788, 2236, 2346, 2348, 2778, 3335, 3779, 11126, 11133, 11148, 11177, 11222, 11238, 11279, 11339, 11369, 11579, 11666, 11677, 11679, 11699
Offset: 1

Views

Author

David A. Corneth, Aug 23 2018

Keywords

Comments

A299690 can be used to find terms for this sequence below some bound by prepending ones to terms while staying below that bound so the additive and multiplicative root that term matches.
For example, 27 is in A299690 and has multiplicative root 4. 27 has the additive root 9. Prepending 4 ones gives the number 111127 which has multiplicative root 4, the same as 27 has, but it also has an additive root of 4. Furthermore, the digits are in nondecreasing order hence is in this sequence.

Crossrefs

Cf. A009994, A010888, A031347, A064702, A277061, A299690.

Programs

  • PARI
    is(n) = my(cn=n); d=digits(n); if(d!=vecsort(d), return(0)); while(cn>9, d=digits(cn); cn=prod(i=1, #d, d[i])); cn-1 == (n-1)%9 || n == 0
Showing 1-3 of 3 results.

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

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