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.

A326811 Numbers in A326806 whose sum of digits is not a power of 10 and are not of the form 5*10^k or 6*10^k.

Original entry on oeis.org

0, 6667, 58824, 8823529412, 5263157894737, 19607843137255, 65217391304348, 98360655737705, 746268656716418, 4761904761904762, 8955223880597015, 58823529411764706, 1369863013698630137, 60240963855421686747, 3061224489795918367347, 34090909090909090909091
Offset: 1

Views

Author

Chai Wah Wu, Oct 19 2019

Keywords

Comments

A326806 = A326811 UNION A326833 UNION A090019 UNION A093143. Note that several terms (e.g. a(10), a(13), a(17)-a(19)) look like the rounding off of a periodic sequence, i.e. yxxxa9xxxa9xxxa9... rounded off to yxxxa9xxxa9xxxb, where b = a+1. Perhaps these can be considered near-cyclic numbers? - Chai Wah Wu, Oct 21 2019

Links

Crossrefs

Cf. A326806, A326833, A090019, A093143.

Extensions

More terms from Chai Wah Wu, Oct 21 2019

A326833 Numbers whose sum of digits is a power of 10.

Original entry on oeis.org

1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 208, 217, 226, 235, 244, 253, 262, 271, 280, 307, 316, 325, 334, 343, 352, 361, 370, 406, 415, 424, 433, 442, 451, 460, 505, 514, 523, 532, 541, 550, 604, 613
Offset: 1

Views

Author

Alois P. Heinz, Oct 20 2019

Keywords

Links

Crossrefs

Subsequence of A326806.
Cf. A007953, A017173, A028838, A052224, A328560.

Programs

  • Maple
    q:= n-> (m-> m>0 and m=10^ilog[10](m))(add(i, i=convert(n, base, 10))):
select(q, [$1..1000])[];
  • PARI
    isok(n) = my(s=sumdigits(n), k); (s==1) || (s==10) || (ispower(s,,&k) && (k==10)); \\ Michel Marcus, Oct 21 2019

A329271 Numbers k such that k multiplied by the product of its divisors contains k as a substring.

Original entry on oeis.org

1, 5, 6, 10, 16, 24, 25, 30, 36, 40, 50, 51, 60, 70, 76, 90, 92, 100, 125, 176, 195, 240, 249, 250, 363, 375, 376, 430, 490, 500, 501, 510, 546, 556, 560, 568, 570, 600, 620, 624, 625, 648, 680, 730, 749, 750, 760, 810, 875, 909, 930, 972, 975, 976, 990, 999, 1000, 1001, 1010, 1636, 1680, 1930, 2354, 2400, 2490, 2500, 2510, 2512, 2943, 3000
Offset: 1

Views

Author

Scott R. Shannon, Nov 10 2019

Keywords

Comments

Inspired by A328095. To avoid all primes being in the sequence the divisors of k includes k itself.
Contains 10^k, 5*10^k and 6*10^k for all k, 3*10^k, 4*10^k, 7*10^k and 9*10^k for all odd k. - Robert Israel, Nov 11 2019

Examples

			16 is in the sequence as the divisors of 16 are 1,2,4,8,16, and 16*(1*2*4*8*16) = 16*1024 = 16384, and '16384' contains '16' as a substring.
30 is in the sequence as the divisors of 30 are 1,2,3,5,6,10,15,30, and 30*(1*2*3*5*6*10*15*30) = 30*810000 = 24300000, and '24300000' contains '30' as a substring.

Links

  • Scott R. Shannon, Table of n, a(n) for n = 1..1000. Note when searching for these numbers one needs to use arbitrary precision packages; the product for 24570000 has 1486 digits.

Crossrefs

Cf. A007955, A328095, A326806, A328544.
The sequence of primes contained in their squares is A115738.

Programs

  • Magma
    a:=[]; for k in [1..3000] do t:=IntegerToString(k*(&*Divisors(k))); s:=IntegerToString(k); if s in t then Append(~a,k); end if; end for; a; // Marius A. Burtea, Nov 10 2019
  • Mathematica
    f[n_] := n^(1+DivisorSigma[0, n]/2); aQ[n_] := SequenceCount[IntegerDigits[f[n]], IntegerDigits[n]] > 0; Select[Range[3000], aQ] (* Amiram Eldar, Nov 10 2019 *)

A307751 Numbers k such that the number m multiplied by the product of all its digits contains k as a substring, where m = k multiplied by the product of all its digits.

Original entry on oeis.org

0, 1, 5, 6, 7, 11, 19, 79, 84, 111, 123, 176, 232, 396, 1111, 11111, 111111, 331788, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111
Offset: 1

Views

Author

Scott R. Shannon, Nov 10 2019

Keywords

Comments

Inspired by A328095. Like A328095 this sequence contains all the repunits. These numbers could be called 'Two-step Revenant numbers'. It is unknown if 331788 is the last non-repunit.

Examples

			79 is in the sequence as m = 79*7*9 = 4977, and 4977*4*9*7*7 = 8779428, and '8779428' contains '79' as a substring.
331788 is in the sequence as m = 331788*3*3*1*7*8*8 = 1337769216, and 1337769216*1*3*3*7*7*6*9*2*1*6 = 382291633317888, and '382291633317888' contains '331788' as a substring.

Links

  • Eric Angelini, Revenant Numbers, Cinquante Signes, Oct 19 2019.
  • Eric Angelini, Revenant Numbers, Cinquante Signes, Oct 19 2019. [Cached copy, pdf file, with permission]

Crossrefs

Cf. A328095, A326806, A328544.

Programs

  • Magma
    a:=[0]; f:=func; for k in [1..1200000] do t:=IntegerToString(f(f(k))); s:=IntegerToString(k); if s in t then Append(~a,k); end if; end for; a; // Marius A. Burtea, Nov 10 2019
  • Mathematica
    f[n_] := n * Times @@ IntegerDigits[n]; aQ[n_] := SequenceCount[IntegerDigits[ f[f[n]] ], IntegerDigits[n]] > 0; Select[Range[0, 10^6], aQ] (* Amiram Eldar, Nov 10 2019 *)

Extensions

a(24)-a(27) from Giovanni Resta, Nov 15 2019
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.