A050757 -id:A050757 - cp's OEIS frontend

A050758 Primes containing at least one pair of consecutive equal digits.

11, 113, 199, 211, 223, 227, 229, 233, 277, 311, 331, 337, 433, 443, 449, 499, 557, 577, 599, 661, 677, 733, 773, 811, 877, 881, 883, 887, 911, 977, 991, 997, 1009, 1033, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1223, 1229

Offset: 1

Patrick De Geest, Sep 15 1999

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A043096, A000040, A050757, A029743.

Select[Prime[Range[205]],MemberQ[Differences[IntegerDigits[#]],0]&] (* Jayanta Basu, May 31 2013 *)
Select[Prime[Range[300]],SequenceCount[IntegerDigits[#],{x_,x_}]>0&] (* The program uses the SequenceCount function from Mathematica version 10 *) (* Harvey P. Dale, Feb 20 2016 *)

is(n)=my(d=digits(n)); for(i=2,#d,if(d[i]==d[i-1], return(isprime(n)))); 0 \\ Charles R Greathouse IV, Aug 29 2015

a(n) ~ n log n. - Charles R Greathouse IV, Aug 29 2015

A050784 Palindromic primes containing no pair of consecutive equal digits.

Original entry on oeis.org

2, 3, 5, 7, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 12421, 12721, 12821, 13831, 13931, 14341, 14741, 15451, 16061, 16361, 16561, 17471, 17971, 18181, 18481, 19391, 19891, 30103, 30203

Offset: 1

Patrick De Geest, Sep 15 1999

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A002385, A050783, A030147, A050757, A046075.

nextL:= proc(L) local V,j,n,k;
  n:= LinearAlgebra:-Dimension(L);
  V:= L;
  for j from n to 1 by -1 do
    V[j]:= V[j]+1;
    if j > 1 then if V[j] = V[j-1] then V[j]:= V[j]+1 fi
    elif member(V[j],[2,8]) then V[j]:= V[j]+1
    elif member(V[j],[4,5,6]) then V[j]:= 7
    fi;
    if V[j] <= 9 then
      for k from j+1 to n do if (k-j)::odd then V[k]:= 0 else V[k]:= 1 fi od;
      return V
    fi;
  od;
  Vector(n+1, i -> i mod 2)
end proc:
Pali:= proc(L)
  local i,n;
  n:= LinearAlgebra:-Dimension(L);
  add(L[i]*10^(2*n-i-1),i=1..n)+add(L[i]*10^(i-1),i=1..n-1)
end proc:
V:= <5>: Res:= 2,3,5: count:= 3:
while count < 100 do
  V:= nextL(V);
  x:= Pali(V);
  if isprime(x) then count:= count+1; Res:= Res, x fi;
od:
Res; # Robert Israel, Feb 07 2019

Select[Prime[Range[3280]],Reverse[x=IntegerDigits[#]]==x&&FreeQ[Differences[x],0]&] (* Jayanta Basu, Jun 01 2013 *)

cp's OEIS Frontend

A050758 Primes containing at least one pair of consecutive equal digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula