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.

Previous Showing 61-70 of 97 results. Next

A336986 Numbers that are not Colombian and not Bogotá.

Original entry on oeis.org

2, 6, 8, 10, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 87, 89, 90, 91
Offset: 1

Views

Author

Bernard Schott, Aug 22 2020

Keywords

Comments

Equivalently, numbers m that are of the form k + sum of digits of k for some k (A176995), but are not of the form q * product of digits of q for any q.
As repunits are trivially Bogotá numbers, there are not repunits in the data.
A336983, A336984, A336985 and this sequence form a partition of the set of positive integers N*.

Examples

			13 = 11 + (1+1) is not Colombian and 13 is not of the form q * product of digits of q for any q <= 13, so 13 is not a Bogotá number, hence 13 is a term.
39 = 33 + (3+3) is not Colombian but 39 = 13 * (1*3) is a Bogotá number, hence 39 is not a term.
42 = 21 * (2*1) is a Bogotá number but there does not exist k < 42 such that 42 = k + sum of digits of k, hence 42 is a Colombian number and 42 is not a term.

Links

Crossrefs

Cf. A003052 (Colombian), A176995 (not Colombian), A336826 (Bogotá), A336983 (Bogotá and not Colombian), A336984 (Bogotá and Colombian), A336985 (Colombian not Bogotá), this sequence (not Colombian and not Bogotá).

Programs

  • Mathematica
    m = 100; Intersection[Select[Union[Table[n + Plus @@ IntegerDigits[n], {n, 1, m}]], # <= m &], Complement[Range[m], Select[Union[Table[n * Times @@ IntegerDigits[n], {n, 1, m}]], # <= m &]]] (* Amiram Eldar, Aug 22 2020 *)
  • PARI
    lista(nn) = Vec(setintersect(Set(vector(nn, k, k+sumdigits(k))), setminus([1..nn], Set(vector(nn, k, k*vecprod(digits(k))))))); \\ Michel Marcus, Aug 23 2020

A349831 Even numbers in the intersection of A228082 and A349829.

Original entry on oeis.org

0, 2, 10, 12, 14, 16, 22, 24, 26, 28, 34, 36, 38, 40, 44, 50, 58, 60, 62, 66, 68, 70, 72, 74, 76, 82, 84, 92, 94, 96, 98, 106, 108, 110, 114, 118, 120, 122, 126, 132, 134, 136, 140, 146, 154, 156, 158, 162, 164, 170, 174, 176, 178, 186, 188, 190, 196, 198, 202, 204, 206, 210, 214, 216, 218, 222
Offset: 1

Views

Author

N. J. A. Sloane, Jan 07 2022

Keywords

Comments

Even numbers that are "generated" (in Kaprekar's sense) in both bases 2 and 4.

Crossrefs

Cf. A003052, A228082, A349829, A349830, A349832.
A230624 is a subsequence.
A row of A350601.

A349832 Even numbers that are "generated" (in Kaprekar's sense) in all three bases 2, 4, and 6.

Original entry on oeis.org

0, 2, 10, 14, 16, 22, 24, 28, 34, 36, 38, 44, 50, 58, 60, 62, 66, 68, 72, 74, 76, 82, 84, 92, 94, 96, 98, 106, 108, 110, 118, 120, 122, 126, 132, 134, 136, 140, 146, 154, 156, 158, 162, 164, 170, 176, 178, 186, 196, 198, 202, 206, 210, 214, 216, 222, 228, 234, 238, 244, 246, 252, 256, 258, 260
Offset: 1

Views

Author

N. J. A. Sloane, Jan 07 2022

Keywords

Comments

Using Max Alekseyev's PARI "Gen" program (see A010061), we run
vector(500,k,length(Gen(k,2))),
vector(500,k,length(Gen(k,4))), and
vector(500,k,length(Gen(k,6)))
to find the numbers that are generated in bases 2, 4, and 6, and then take the even numbers that are common to all three lists.

Crossrefs

Cf. A003052, A010061, A228082, A349829, A349830, A349831, A349833.
A230624 is a subsequence.
A row of A350601.

A349833 Even numbers that are "generated" (in Kaprekar's sense) in all four bases 2, 4, 6, and 8.

Original entry on oeis.org

0, 2, 10, 14, 22, 24, 28, 36, 38, 44, 50, 58, 60, 62, 66, 68, 74, 76, 82, 84, 92, 94, 96, 98, 106, 110, 118, 120, 122, 132, 134, 136, 140, 154, 156, 158, 162, 170, 176, 178, 186, 196, 198, 206, 210, 214, 216, 222, 228, 234, 244, 246, 252, 258, 260, 262, 264, 268, 274, 284, 286
Offset: 1

Views

Author

N. J. A. Sloane, Jan 07 2022

Keywords

Comments

Using Max Alekseyev's PARI "Gen" program (see A010061), we run
vector(500,k,length(Gen(k,2))),
vector(500,k,length(Gen(k,4))),
vector(500,k,length(Gen(k,6))),
vector(500,k,length(Gen(k,8))),
to find the numbers that are generated in bases 2, 4, 6, and 8, and then take the even numbers that are common to all four lists.

Links

Crossrefs

Cf. A003052, A010061, A228082, A349829, A349830, A349831, A349832.
A230624 is a subsequence.
A row of A350601.

A377422 Numbers that can be expressed as (m + sum of digits of m) in exactly four ways.

Original entry on oeis.org

1000000000000000000000102, 1000000000000000000000104, 1000000000000000000000106, 1000000000000000000000108, 1000000000000000000000110, 1000000000000000000000112, 1000000000000000000000114, 2000000000000000000000103, 2000000000000000000000105, 2000000000000000000000107, 2000000000000000000000109
Offset: 1

Views

Author

Daniel Mondot, Oct 27 2024

Keywords

Comments

Numbers k such that A230093(k) = 0 give A003052, the Self or Colombian numbers.
Numbers k such that A230093(k) = 1 give A225793.
Numbers k such that A230093(k) = 2 give A230094.
Numbers k such that A230093(k) = 3 give A230100.
Numbers k such that A230093(k) = 4 give this sequence.

Examples

			There are exactly four numbers, 999999999999999999999894, 999999999999999999999903, 1000000000000000000000092, and 1000000000000000000000101, whose image under n->f(n) is 1000000000000000000000104, so 1000000000000000000000104 is a member of the sequence.

Links

Crossrefs

Cf. A230100, A006064, A062028, A230093.

Extensions

Corrected by Daniel Mondot, Apr 17 2025

A377423 Distinct values of the number of integers between consecutive self numbers (A163139), in order of occurrence.

Original entry on oeis.org

1, 10, 14, 27, 40, 53, 66, 79, 92, 105, 118, 100, 117, 130, 143, 156, 169, 182, 195, 208, 23, 89, 203, 220, 233, 246, 259, 272, 285, 298, 34, 78, 293, 306, 323, 336, 349, 362, 375, 388, 45, 67, 383, 396, 409, 426, 439, 452, 465, 478, 56, 473, 486, 499
Offset: 1

Views

Author

Daniel Mondot, Oct 27 2024

Keywords

Comments

Each new value is typically found between self numbers located around 10^k, for some k.
This sequences exhibits interesting patterns, for instance, many new numbers are 13 apart.

Examples

			Between the first 2 self numbers 1 and 3, there is 1 integer. So 1 is in the sequence
The next new gap is between 9 and 20, with 10 integers, so 10 is in the sequence.
The next new gap is between 1006 and 1021, with 14 integers, so 14 is in the sequence.

Links

Crossrefs

Cf. A003052, A163128, A163139, A225793, A230093, A230094, A377422, A377472, A377473.

Formula

a(n) = A377473(n)-1. - Daniel Mondot, Apr 17 2025

A377474 Indices where new terms arise among first differences of Colombian or self numbers (A377472).

Original entry on oeis.org

1, 5, 103, 984, 9785, 97786, 977787, 9777788, 97777789
Offset: 1

Views

Author

M. F. Hasler, Oct 30 2024

Keywords

Comments

See A377473 for the distinct values of the first differences in the order they appear for the first time.

Examples

			The first value, A377472(1) = 2, appears obviously at index a(1) = 1.
The next three values are the same, but at index a(2) = 5 we have a new, distinct value A377472(5) = 11 = A377423(2).
The next distinct value is A377472(103) = 15 = A377423(3), so a(3) = 103.
Then the next new value is A377472(984) = 28 = A377423(4), so a(4) = 984.
The next new value is A377472(9785) = 41 = A377423(5), so a(5) = 9785.
Then, at n = 97786 = a(6), we have A377472(n) = 54 = A377423(6).
Only at n = 977787 = a(7), we have a new value, A377472(n) = 67 = A377423(7).
At n = 9777788 = a(8), we have the next new value, A377472(n) = 80 = A377423(8).

Crossrefs

Cf. A003052 (Colombian numbers), A377472 (1st differences of Colombian numbers), A377473 (distinct values of A377472 in order of appearance), A377423 (= A377473 - 1).

Programs

  • PARI
    A377473_upto(N=9, show=1)={my(o, c, d, L=List()); for(n=1+o=1, oo, is_A003052(n)||next; c++; if(!setsearch(L, d=n-o), show && printf("%d, ",[c,d]); listput(L,c); #L

Formula

a(n+1) = a(n) + 88*10^(n-1) + 1 for n = 3, 4, ..., 7 at least.

Extensions

a(9) from Daniel Mondot, May 01 2025

A380713 Lesser of twin self primes, i.e., smaller member of the pair of self primes differing by 2.

Original entry on oeis.org

3, 5, 18521, 19421, 39827, 44621, 49121, 57221, 59627, 65927, 84221, 86627, 129221, 139121, 149627, 153521, 172421, 182927, 207521, 209927, 231821, 238727, 251621, 254927, 264827, 274121, 277427, 289127, 308927, 317321, 319727, 321821, 327827, 329627, 330821
Offset: 1

Views

Author

Shyam Sunder Gupta, Mar 27 2025

Keywords

Links

Crossrefs

Cf. A003052, A001359, A374101, A380715.

A380715 Greater of twin self primes, i.e., larger member of the pair of self primes differing by 2.

Original entry on oeis.org

5, 7, 18523, 19423, 39829, 44623, 49123, 57223, 59629, 65929, 84223, 86629, 129223, 139123, 149629, 153523, 172423, 182929, 207523, 209929, 231823, 238729, 251623, 254929, 264829, 274123, 277429, 289129, 308929, 317323, 319729, 321823, 327829, 329629, 330823
Offset: 1

Views

Author

Shyam Sunder Gupta, Mar 27 2025

Keywords

Links

Crossrefs

Cf. A003052, A006512, A382380, A380713.

A225048 Numbers that cannot be expressed as n plus the sum of the squared digits of n for any integer n.

Original entry on oeis.org

1, 3, 4, 5, 7, 8, 9, 10, 14, 15, 16, 18, 19, 21, 22, 25, 27, 28, 29, 32, 33, 34, 35, 37, 38, 40, 43, 46, 47, 48, 49, 50, 52, 55, 57, 60, 61, 63, 64, 65, 70, 71, 73, 74, 78, 79, 82, 84, 85, 88, 89, 91, 92, 93, 94, 97, 99, 100, 104, 106, 109, 110, 115, 120, 122
Offset: 1

Views

Author

Kevin L. Schwartz and Christian N. K. Anderson, Apr 25 2013

Keywords

Comments

A natural extension of the Self or Colombian numbers (A003052).
Up to 144, there are more numbers that cannot be expressed in this way than numbers that can. Thereafter, there are always more numbers that can.

Examples

			26 is not in the sequence, because 21+2^2+1^2=26. However, no such solution exists for 25 or 27.

Links

Crossrefs

Cf. A003052, A003219, A003132, A062028, A066568.

Programs

  • Mathematica
    nn=122;Complement[Range[nn],Table[n+Total[IntegerDigits[n]^2],{n,nn}]] (* Jayanta Basu, May 05 2013 *)
  • R
    digsqsum<-function(x) sum(as.numeric(unlist(strsplit(as.character(x),split="")))^2)
which(is.na(match(1:1000,1:1000+sapply(1:1000,digsqsum)))
Previous Showing 61-70 of 97 results. Next

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

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