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 1-5 of 5 results.

A036928 Composite numbers whose prime factors contain no digits other than 0 and 1.

Original entry on oeis.org

121, 1111, 1331, 10201, 12221, 14641, 111221, 112211, 134431, 161051, 1021211, 1030301, 1112221, 1223431, 1234321, 1478741, 1771561, 10212211, 11121011, 11233321, 11333311, 12101111, 12234431, 13457741, 13577531, 16266151
Offset: 1

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A020449, A036302-A036325, A036929.

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020449} (p/(p - 1)) - Sum_{p in A020449} 1/p - 1 = 0.0102023428... . - Amiram Eldar, May 18 2022

Extensions

Description clarified by Ray Chandler, Nov 07 2008

A036945 Smallest n-digit prime containing only the digits 4 and 9, or 0 if no such prime exists.

Original entry on oeis.org

0, 0, 449, 4999, 44449, 444449, 4444949, 44444999, 444499949, 4444444999, 44444449949, 444444494449, 4444449444949, 44444444449499, 444444444499499, 4444444444444999, 44444444444444999, 444444444449449949
Offset: 1

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Examples

			44449 is the least prime of 5 digits containing just digits 4 and 9 so a(5) = 44449. - _David A. Corneth_, Oct 10 2019

Links

Crossrefs

Cf. A036229, A020466, A036319, A036929-A036951.

Programs

  • Mathematica
    Join[{0,0},Table[SelectFirst[10*FromDigits[#]+9&/@Tuples[{4,9},n],PrimeQ],{n,2,20}]] (* Harvey P. Dale, Aug 20 2021 *)
  • PARI
    a(n) = my(s=4*(10^(n)-1)/9);forstep(i=1, 2^n-1, 2, fr = fromdigits(5 * binary(i)) + s; if(isprime(fr), return(fr))); 0 \\ David A. Corneth, Oct 10 2019

A165508 Numbers k such that 10^k + 111 is prime.

Original entry on oeis.org

2, 4, 184, 460, 784, 3248, 5194, 92386, 156428, 228208
Offset: 1

Views

Author

Rick L. Shepherd, Sep 21 2009

Keywords

Comments

Terms must be congruent to 2 or 4 mod 6. Other than the first term, which produces 10^2 + 111 = 211, these terms produce primes whose decimal representation is 1 111 concatenated. These are only known to be highly probable primes for 184 and beyond. No more terms up to 15000.
a(8) > 55000. - Tyler NeSmith, Jul 10 2021
The corresponding primes have digit sum 4 (A062339). - Jeppe Stig Nielsen, Feb 10 2023
a(9) > 10^5. - Jeppe Stig Nielsen, Feb 11 2023
a(11) > 6.6*10^5. - Boyan Hu, Nov 14 2024

Examples

			As 10111 = 10^4 + 111 is a prime, 4 is a term.

Crossrefs

Cf. A096912, A157711, A062339, A020449, A036929, A161786.

Programs

Extensions

a(8) from Jeppe Stig Nielsen, Feb 10 2023
a(9)-a(10) from Boyan Hu, Oct 23 2024

A168588 Smallest p(n)-digit prime with digit sum n, and made up of digits 0 and 1 only, where p(n)=A000040(n) (or 0, if no such prime exists).

Original entry on oeis.org

0, 101, 0, 1011001, 10000110011, 0, 10000000010101111, 1000000000001111111, 0, 10000000000000000101101111101, 1000000000000000000011111110111, 0, 10000000000000000000000000011111111110101, 1000000000000000000000000000110111111011111
Offset: 1

Views

Author

Lekraj Beedassy, Nov 30 2009

Keywords

Comments

a(3n) = 0.

Links

Crossrefs

Cf. A036929

Programs

  • Maple
    g:= proc(L) local i,m;
  m:= -1;
  for i from 1 do
     if L[i] = 1 then
       if m = -1 then m:= i fi;
       if L[i+1] = 0 then
         return [1$(i-m),0$(m-1),0,1,op(L[i+2..-1])]
       fi
     fi
  od
end proc:
f:= proc(n) local L,x,pn,i;
  if n mod 3 = 0 then return 0 fi;
  pn:= ithprime(n);
  L:= [1$(n-1),0$(pn-n),1];
  do
    x:= add(L[i]*10^(i-1),i=1..pn);
    if isprime(x) then return x fi;
    L:= g(L);
  od
end proc:
map(f, [$1..16]); # Robert Israel, Feb 01 2021

Extensions

Extended by Ray Chandler, Dec 03 2009

A261173 Table read by antidiagonals: T(n,k) = smallest prime p containing only digits 0 and 1 with n 0's and k 1's, or 0 if no such p exists.

Original entry on oeis.org

11, 0, 101, 0, 0, 0, 0, 10111, 0, 0, 0, 101111, 0, 0, 0, 0, 0, 0, 1011001, 0, 0, 0, 11110111, 0, 10011101, 10010101, 0, 0, 0, 101111111, 101101111, 0, 100100111, 101001001, 0, 0, 0, 0, 1010111111, 1001110111, 0, 1000011011, 1000001011, 0, 0
Offset: 0

Views

Author

Felix Fröhlich, Aug 10 2015

Keywords

Comments

T(n, k) = 0 if k is a term of A008585.
T(0, k) != 0 iff k is a term of A004023.
T(1, k) = A157709(k-2) for all k >= 4.
T(n, 2) != 0 iff A062397(n+1) is prime.
a(n) is in A168586 iff it is the smallest p in T with A007953(p) = k.

Examples

			Table T(n, k) starts
     k = 2        3        4        5
      -------------------------------------
n = 0 |  11       0        0        0
n = 1 |  101      0        10111    101111
n = 2 |  0        0        0        0
n = 3 |  0        0        1011001  10011101

Links

Crossrefs

Cf. A020449, A036929.

Programs

  • PARI
    a(n, k) = i=0; forprime(p=10^(n+k-1), (10^(n+k)-1)/9, if(vecmax(digits(p))==1 && sumdigits(p)==k, return(p); i++; break)); if(i==0, return(0))
table(row, col) = for(x=0, row, for(y=2, col, print1(a(x, y), " ")); print(""))
table(4, 5) \\ print 5 X 4 table

Extensions

More terms from Alois P. Heinz, Aug 17 2015
Showing 1-5 of 5 results.

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