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 1-10 of 13 results. Next

A262582 Concatenation of the numbers from 1 to n but omitting 12.

Original entry on oeis.org

1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 12345678910, 1234567891011, 123456789101113, 12345678910111314, 1234567891011131415, 123456789101113141516, 12345678910111314151617, 1234567891011131415161718, 123456789101113141516171819, 12345678910111314151617181920
Offset: 1

Views

Author

N. J. A. Sloane, Sep 25 2015

Keywords

Comments

The first (probable) prime in this sequence is a(960) = 1234567891011131415...961 (ending in 961), found by David Broadhurst, Sep 28 2015.
No other primes through a(10000). - Robert Price, Nov 04 2018

Crossrefs

Cf. A007908, A262299, A262300, A262571-A262582.
See A262300 for more about this problem.

Programs

  • Mathematica
    Module[{nn=30, c}, c=Drop[Range[nn], {12}]; Table[FromDigits[Flatten[IntegerDigits/@Take[c, n]]], {n, nn - 1}]] (* Vincenzo Librandi, Nov 05 2018 *)

A262300 Let S(n,k) denote the number formed by concatenating the decimal numbers 1,2,3,...,k, but omitting n; a(n) is the smallest k for which S(n,k) is prime, or -1 if no term in S(n,*) is prime.

Original entry on oeis.org

2, 3, 7, 9, 11, 7, 11, 1873, 19, 14513, 13, 961
Offset: 1

Views

Author

N. J. A. Sloane and Jerrold B. Tunnell, Sep 27 2015

Keywords

Comments

Sep 28 2015: David Broadhurst has found a(10) = 14513, a(12) = 961, a(14) = 653, a(16) = 5109, a(17) = 493, a(18) = 757, and a(20) = 1313. All these correspond to probable primes.
It is easy to check that a(19)=29.
So the sequence begins 2, 3, 7, 9, 11, 7, 11, 1873, 19, 14513, 13, 961, ???, 653, ???, 5109, 493, 757, 29, 1313, ...
a(13) is either -1 or greater than 40000. - Robert Price, Nov 03 2018

Examples

			a(5) = 11 because the smallest prime in S(5,*) (A262575) is 123467891011.
a(8) = 1873 (corresponding to the 6364-digit probable prime 1234567910111213...1873) was found by David Broadhurst on Sep 27 2015.
a(9) = 19 because the smallest prime in S(9,*) is 1234567810111213141516171819.
a(10) = 14513 (corresponding to the 61457-digit probable prime 123456789111213...14513) was found by David Broadhurst on Sep 28 2015.

Crossrefs

Cf. A262299.
See A262571-A262582 for the sequences S(1,*) through S(12,*).
See also A007908 (which plays the role of S(0,*)).
For the primes in S(1,*) and S(2,*) see A089987, A262298.

Programs

  • Mathematica
    A262300[n_] := Module[{k = 1}, While[! PrimeQ[FromDigits[Flatten[Map[IntegerDigits, Complement[Range[k], {n}]]]]], k++]; k];
Table[A262300[n], {n, 12}]  (* Robert Price, Oct 27 2018 *)
  • PARI
    s(n, k) = my(s=""); for(x=1, k, if(x!=n, s=concat(s, x))); eval(Str(s))
a(n) = for(k=1, oo, my(s=s(n, k)); if(ispseudoprime(s), return(k))) \\ Felix Fröhlich, Oct 27 2018

Extensions

a(8) was found by David Broadhurst, Sep 27 2015. On Sep 28 2015 David Broadhurst also found a(10), a(12), a(14), a(16), a(17), a(18), and a(20).

A262571 Concatenation of the numbers from 2 to n.

Original entry on oeis.org

2, 23, 234, 2345, 23456, 234567, 2345678, 23456789, 2345678910, 234567891011, 23456789101112, 2345678910111213, 234567891011121314, 23456789101112131415, 2345678910111213141516, 234567891011121314151617, 23456789101112131415161718, 2345678910111213141516171819
Offset: 2

Views

Author

N. J. A. Sloane, Sep 25 2015

Keywords

Crossrefs

For primes in this sequence see A089987.
Cf. A007908, A262299, A262572-A262582.
See A262300 for more about this problem.

Programs

  • Magma
    [Seqint(Reverse(&cat[Reverse(Intseq(k)): k in [2..n]])): n in [2..20]]; // Vincenzo Librandi, Oct 29 2018
  • Mathematica
    Table[FromDigits[Flatten[IntegerDigits[Range[2, n]]]], {n, 2, 19}]  (* Robert Price, Oct 28 2018 *)
  • Python
    def a(n): return int("".join(map(str, range(2, n+1))))
print([a(n) for n in range(2, 20)]) # Michael S. Branicky, Feb 23 2021

A262572 Concatenation of the numbers from 1 to n but omitting 2.

Original entry on oeis.org

1, 13, 134, 1345, 13456, 134567, 1345678, 13456789, 1345678910, 134567891011, 13456789101112, 1345678910111213, 134567891011121314, 13456789101112131415, 1345678910111213141516, 134567891011121314151617, 13456789101112131415161718, 1345678910111213141516171819, 134567891011121314151617181920
Offset: 1

Views

Author

N. J. A. Sloane, Sep 25 2015

Keywords

Crossrefs

For primes see A262298.
Cf. A007908, A262299, A262571-A262582.
See A262300 for more about this problem.

Programs

  • Mathematica
    DeleteDuplicates[Table[FromDigits[Flatten[IntegerDigits[Complement[Range[n], {2}]]]], {n, 20}]] (* Robert Price, Nov 05 2018 *)

A262575 Concatenation of the numbers from 1 to n but omitting 5.

Original entry on oeis.org

1, 12, 123, 1234, 12346, 123467, 1234678, 12346789, 1234678910, 123467891011, 12346789101112, 1234678910111213, 123467891011121314, 12346789101112131415, 1234678910111213141516, 123467891011121314151617, 12346789101112131415161718, 1234678910111213141516171819, 123467891011121314151617181920
Offset: 1

Views

Author

N. J. A. Sloane, Sep 25 2015

Keywords

Comments

The only primes among the first 98 terms are 123467891011 and 123467891011121314151617. See A262552 for further primes in this sequence.

Crossrefs

Cf. A007908, A262299, A262571-A262582.
See A262300 for more about this problem.
For primes see A262552.

Programs

  • Mathematica
    DeleteDuplicates[Table[FromDigits[Flatten[IntegerDigits[Complement[Range[n], {5}]]]], {n, 20}]] (* Robert Price, Nov 05 2018 *)
Join[{1,12,123,1234},Table[FromDigits[Flatten[IntegerDigits/@Drop[Range[n],{5}]]],{n,6,20}]] (* Harvey P. Dale, Jan 28 2024 *)

A262581 Concatenation of the numbers from 1 to n but omitting 11.

Original entry on oeis.org

1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 12345678910, 1234567891012, 123456789101213, 12345678910121314, 1234567891012131415, 123456789101213141516, 12345678910121314151617, 1234567891012131415161718, 123456789101213141516171819, 12345678910121314151617181920
Offset: 1

Views

Author

N. J. A. Sloane, Sep 25 2015

Keywords

Comments

There are only two primes among the first 98 terms, namely 123456789101213 and
1234567891012131415161718192021222324252627282930313233343536\
373839404142434445464748495051525354555657585960616263.
Does this sequence contain any other primes?
No other primes through a(10000). - Robert Price, Nov 05 2018

Crossrefs

Cf. A007908, A262299, A262571-A262582.
See A262300 for more about this problem.

Programs

  • Mathematica
    DeleteDuplicates[Table[FromDigits[Flatten[IntegerDigits[Complement[Range[n], {11}]]]], {n, 20}]] (* Robert Price, Nov 05 2018 *)
  • PARI
    terms(n) = my(s="", i=0); for(k=1, n, if(k!=11, s=concat(s, Str(k)); print1(eval(s), ", "); i++); if(i==n, break))
/* Print initial 20 terms as follows */
terms(20) \\ Felix Fröhlich, Nov 05 2018

A262573 Concatenation of the numbers from 1 to n but omitting 3.

Original entry on oeis.org

1, 12, 124, 1245, 12456, 124567, 1245678, 12456789, 1245678910, 124567891011, 12456789101112, 1245678910111213, 124567891011121314, 12456789101112131415, 1245678910111213141516, 124567891011121314151617, 12456789101112131415161718, 1245678910111213141516171819, 124567891011121314151617181920
Offset: 1

Views

Author

N. J. A. Sloane, Sep 25 2015

Keywords

Comments

The only prime among the first 98 terms is a(6) = 124567. Does the sequence contain any other primes?
No other primes through a(10000). - Robert Price, Nov 04 2018

Crossrefs

Cf. A007908, A262299, A262571-A262582.
See A262300 for more about this problem.

Programs

  • Mathematica
    DeleteDuplicates[Table[FromDigits[Flatten[IntegerDigits[Complement[Range[n], {3}]]]], {n, 20}]] (* Robert Price, Nov 05 2018 *)
Join[{1,12},Table[FromDigits[Join[{1,2},Flatten[IntegerDigits/@Range[4,n]]]],{n,4,20}]] (* Harvey P. Dale, Sep 17 2019 *)

A262574 Concatenation of the numbers from 1 to n but omitting 4.

Original entry on oeis.org

1, 12, 123, 1235, 12356, 123567, 1235678, 12356789, 1235678910, 123567891011, 12356789101112, 1235678910111213, 123567891011121314, 12356789101112131415, 1235678910111213141516, 123567891011121314151617, 12356789101112131415161718, 1235678910111213141516171819, 123567891011121314151617181920
Offset: 1

Views

Author

N. J. A. Sloane, Sep 25 2015

Keywords

Comments

The only prime among the first 98 terms is a(8) = 12356789. Does the sequence contain any other primes?
No other primes through a(10000). - Robert Price, Nov 03 2018

Crossrefs

Cf. A007908, A262299, A262571-A262582.
See A262300 for more about this problem.

Programs

  • Mathematica
    DeleteDuplicates[Table[FromDigits[Flatten[IntegerDigits[Complement[Range[n], {4}]]]], {n, 20}]] (* Robert Price, Nov 05 2018 *)

A262576 Concatenation of the numbers from 1 to n but omitting 6.

Original entry on oeis.org

1, 12, 123, 1234, 12345, 123457, 1234578, 12345789, 1234578910, 123457891011, 12345789101112, 1234578910111213, 123457891011121314, 12345789101112131415, 1234578910111213141516, 123457891011121314151617, 12345789101112131415161718, 1234578910111213141516171819, 123457891011121314151617181920
Offset: 1

Views

Author

N. J. A. Sloane, Sep 25 2015

Keywords

Comments

The only prime among the first 98 terms is a(6) = 123457. Does the sequence contain any other primes?
No additional primes through the first 2000 terms. - Harvey P. Dale, Sep 27 2018
Differs from A132943 at about the 28th terms.
No primes, other than a(6), through a(10000). - Robert Price, Nov 03 2018

Crossrefs

Cf. A132943.
Cf. A007908, A262299, A262571-A262582.
See A262300 for more about this problem.

Programs

  • Mathematica
    Module[{nn=20,c},c=Drop[Range[nn],{6}];Table[FromDigits[Flatten[ IntegerDigits/@ Take[c,n]]],{n,nn-1}]] (* Harvey P. Dale, Sep 27 2018 *)

A262577 Concatenation of the numbers from 1 to n but omitting 7.

Original entry on oeis.org

1, 12, 123, 1234, 12345, 123456, 1234568, 12345689, 1234568910, 123456891011, 12345689101112, 1234568910111213, 123456891011121314, 12345689101112131415, 1234568910111213141516, 123456891011121314151617, 12345689101112131415161718, 1234568910111213141516171819, 123456891011121314151617181920
Offset: 1

Views

Author

N. J. A. Sloane, Sep 25 2015

Keywords

Comments

There are only three primes among the first 98 terms: 123456891011,
12345689101112131415161718192021222324252627282930313233343536373839, and
12345689101112131415161718192021222324252627282930313233343536373839\
40414243444546474849505152535455565758596061626364566676869707172737\
475767778798081828384858687.
Does the sequence contain any other primes?
Yes, PARI reports the next (probable) prime after appending 13097; it has 54655 digits. - Bill McEachen, Oct 13 2015

Crossrefs

Cf. A007908, A262299, A262571-A262582.
See A262300 for more about this problem.

Programs

  • Mathematica
    DeleteDuplicates@ Table[If[n >= 7, FromDigits@ Delete[Flatten[IntegerDigits /@ Range[n + 1]], 7], FromDigits@ Flatten[IntegerDigits /@ Range@ n]], {n, 19}] (* Michael De Vlieger, Oct 13 2015 *)

Formula

(a(n) - a(n-1)) mod 2 = 0 only for n=7. - Altug Alkan, Oct 15 2015
Showing 1-10 of 13 results. Next

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

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