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.

A254622 Number of zerofree positive integers of at most n digits having product of digits less than or equal to sum of digits.

Original entry on oeis.org

9, 27, 61, 124, 255, 474, 860, 1597, 2726, 4232, 6741, 10391, 16177, 24480, 34926, 47875, 65896, 92255, 139262, 198988, 271642, 357674, 474239, 609442, 773493, 1029477, 1404094, 1857856, 2392385, 3169652, 4059322, 5102419, 6482700, 8041992
Offset: 1

Views

Author

David A. Corneth, Feb 03 2015

Keywords

Comments

See A254621 for the numbers with this property. - Wolfdieter Lang, Feb 23 2015

Links

Crossrefs

Cf. A052382, A062996, A254621.

A274125 Numbers having digits in nondecreasing order and sum of digits greater than or equal to the product of digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1122, 1123, 1124, 11111, 11112, 11113, 11114, 11115, 11116, 11117, 11118, 11119, 11122
Offset: 1

Views

Author

David A. Corneth, Jun 10 2016

Keywords

Comments

Intersection of A062996 and A009994. Permuting the digits of the terms of this sequence gives A254621. Permutations of digits can be found in A261370. The union of A254621 and A011540 is A062996.

Links

Crossrefs

Cf. A062996, A009994.

Programs

  • Mathematica
    upto[nd_] := Sort[FromDigits /@ Reverse /@ Select[ Flatten[ IntegerPartitions[#, nd, Range@ 9] & /@ Range[9 nd], 1], Times @@ # <= Plus @@ # &]]; upto[8] (* Giovanni Resta, Jun 20 2016 *)
  • PARI
    is(n) = my(d=digits(n)); prod(i=1, #d, d[i]) <= vecsum(d) && vecsort(d) == d

A274126 Numbers with digits larger than 1 sorted by product of digits minus sum of digits, then by size.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 24, 222, 25, 33, 26, 27, 34, 223, 28, 29, 35, 44, 224, 2222, 36, 233, 37, 45, 225, 38, 46, 226, 39, 55, 234, 2223, 47, 227, 333, 56, 48, 228, 235, 244, 2224, 22222, 49, 57, 229, 66, 236, 334, 2233, 58, 67, 245, 2225, 237, 59, 68, 335
Offset: 1

Views

Author

David A. Corneth, Jun 10 2016

Keywords

Comments

Let PS(n) be product of digits of n minus sum of digits of n (=-A062329(n)). Then a(n) is PS(A037344(m)) ordered by PS(n) for values of m such that A037344 has its digits in nondecreasing order. If PS(m) some nonzero term m of A002276 exceed some bound, all positive integers t larger than that term without zeros and ones exceed have a larger value for PS(t).
Prepending -A062329(a(n)) or more ones before a(n) gives terms of A274125.
Permuting digits of A274125 gives A254621. Permutations of digits can be found in A261370. The union of A254621 and A011540 is A062996. The b-file lists terms having PS(n) <= 10^6.

Examples

			Suppose we want to order the nondecreasing integers without zeros and ones up to PS(m) = 50. We see that 222222 has PS(222222) = 52, so we only have to check such nondecreasing integers up to 222222. Not all of those must be checked, which is used in the program.
25 is a term. Prepending PS(25) = -A062329(25) = 3 ones before 25 gives 11125, which is a term of A274125. Permuting digits of 11125 gives for example 12511, which is a term of A254621.

Links

Crossrefs

Cf. A011540, A037344, A062329, A062996, A254621, A261370, A274125.

Programs

  • PARI
    See program in link "PARI program".
Showing 1-3 of 3 results.

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

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