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 1-6 of 6 results.

A071363 Largest n-digit prime with strictly increasing digits.

Original entry on oeis.org

7, 89, 569, 5689, 34679, 345689, 1456789, 23456789
Offset: 1

Views

Author

Rick L. Shepherd, May 21 2002

Keywords

Comments

Notice the terms with consecutive digits; search for 23456789 to find several related sequences including A006055, A052017 and A052077.

Examples

			a(1) = A052015(4), a(2) = A052015(15), a(3) = A052015(35), a(4) = A052015(61), ... In short, a(n) = A052015(b(n)) with b = (4, 15, 35, 61, 81, 94, 98, 100). - _M. F. Hasler_, May 03 2017
		

Crossrefs

Subsequence of A052015.

Programs

  • PARI
    A071363(n,u=vectorv(n,i,10^(n-i)))={forvec(d=vector(n,i,[1,9]),isprime(d*u)&&n=d*u,2);n} \\ M. F. Hasler, May 03 2017

A052078 Smallest prime formed by concatenating n consecutive decreasing numbers, 0 if no such prime exists.

Original entry on oeis.org

2, 43, 0, 10987, 76543, 0, 73727170696867, 4645444342414039, 0, 56555453525150494847, 219218217216215214213212211210209, 0, 25242322212019181716151413, 6059585756555453525150494847, 0
Offset: 1

Views

Author

Patrick De Geest, Jan 15 2000

Keywords

Comments

Starting numbers in concatenations are given by A052080.
If n is divisible by 3, a(n)=0. - Harvey P. Dale, Jun 03 2019

Crossrefs

Programs

  • Mathematica
    Table[Min[Select[FromDigits[Flatten[IntegerDigits[#]]]&/@ Partition[ Range[ 1000,1,-1],n,1],PrimeQ]],{n,20}]/.\[Infinity]->0 (* Harvey P. Dale, Jun 03 2019 *)

Extensions

Terms for n>6 calculated by Carlos Rivera and Felice Russo

A052079 Concatenation of n consecutive ascending numbers starting from a(n) produces the smallest possible prime of this form, 0 if no such prime exists.

Original entry on oeis.org

2, 2, 0, 4, 15, 0, 7, 2, 0, 4, 129, 0, 5, 50, 0, 128, 3, 0, 23, 38, 0, 9998, 17, 0, 25, 2, 0, 16, 341, 0, 569, 42, 0, 14, 1203, 0, 2465, 102, 0, 212, 1161, 0, 197
Offset: 1

Views

Author

Patrick De Geest, Jan 15 2000

Keywords

Comments

Next term a(44)=10^348-32 (only probable prime with 15324 digits). a(110)=9999968. If n is divisible by 22 then either a(n)=0 or a(n)=10^x-b for some bJens Kruse Andersen, Feb 03 2003

Examples

			For n = 7 we have a(7) = 7 so the seven consecutive ascending numbers 7,8,9,10,11,12 and 13 concatenated together gives the smallest possible prime of this form, 78910111213.
		

Crossrefs

Programs

  • PARI
    isok(vc) = {my(x=""); for (i=1, #vc, x = concat(x, Str(vc[i]))); ispseudoprime(eval(x));}
    a(n) = if (n % 3, for(i=1, oo, my(vc = vector(n, k, k+i-1)); if (isok(vc), return(i))), 0); \\ Michel Marcus, Mar 04 2021

Extensions

Terms a(7)-a(43) calculated by Carlos Rivera and Felice Russo

A052080 Concatenation of n consecutive descending numbers starting from a(n) produces the smallest possible prime of this form, 0 if no such prime exists.

Original entry on oeis.org

2, 4, 0, 10, 7, 0, 73, 46, 0, 56, 219, 0, 25, 60, 0, 52, 117, 0, 535, 172, 0
Offset: 1

Views

Author

Patrick De Geest, Jan 15 2000

Keywords

Comments

First hard cases occur for n = 22, 88 and 110.
a(22) = 10^1631 + 10 was found by James G. Merickel in Feb 2011.
a(88) = 10^14 + 6.
a(110) = 10^19 + 26 was found by Chris Nash.

Examples

			For n = 8 we have a(8) = 46 so the eight consecutive descending numbers 46,45,44,43,42,41,40 and 39 concatenated together gives the smallest possible prime of this form, 4645444342414039.
		

Crossrefs

Extensions

Terms a(7)-a(21) calculated by Carlos Rivera and Felice Russo

A068697 Smallest prime which is a concatenation of n consecutive odd numbers. If no such prime exists then 0.

Original entry on oeis.org

3, 13, 0, 23252729, 2527293133, 0, 57911131517, 4547495153555759, 0, 135791113151719, 87899193959799101103105107, 0, 23252729313335373941434547, 357911131517192123252729, 0
Offset: 1

Views

Author

Amarnath Murthy, Mar 03 2002

Keywords

Comments

a(3k) = 0.

Examples

			a(4) = 23252729 as a concatenation of 23,25,27 and 29. a(3) = 0 for a concatenation of 3 odd numbers is always a multiple of 3.
		

Crossrefs

Cf. A052077.

Programs

  • Mathematica
    d[n_]:=IntegerDigits[n]; t={3}; Do[If[Mod[m,3]==0,x=0,k=1; While[!PrimeQ[x=FromDigits[Fold[Join,d[k],Table[d[k+2n],{n,m-1}]]]],k++]]; AppendTo[t,x],{m,2,15}]; t (* Jayanta Basu, May 21 2013 *)

Extensions

More terms from Sascha Kurz, Mar 26 2002

A262193 Primes that are a concatenation of ten consecutive numbers.

Original entry on oeis.org

45678910111213, 20212223242526272829, 68697071727374757677, 88899091929394959697, 122123124125126127128129130131, 140141142143144145146147148149, 188189190191192193194195196197, 200201202203204205206207208209, 212213214215216217218219220221
Offset: 1

Views

Author

Altug Alkan, Sep 14 2015

Keywords

Examples

			4_5_6_7_8_9_10_11_12_13 is a prime number.
		

Crossrefs

Programs

  • Mathematica
    Select[FromDigits[Flatten[IntegerDigits[#]]]&/@Partition[Range[300], 10, 1], PrimeQ] (* Vincenzo Librandi, Sep 15 2015 *)
  • PARI
    for(n=1, 1e3, if(isprime(k=eval(Str(n, n+1, n+2, n+3, n+4, n+5, n+6, n+7, n+8, n+9))), print1(k", ")))
Showing 1-6 of 6 results.