A078790 Palindromic primes with successive increasing difference: a(k)-a(k-1) < a(k+1)- a(k).

2, 5, 11, 101, 313, 727, 10301, 19891, 30103, 70207, 1003001, 1936391, 3001003, 7014107, 100030001, 193191391, 300020003, 700020007, 10000500001, 19301110391, 30000500003, 70005450007, 1000008000001, 1930022200391, 3000002000003, 7000005000007, 100000323000001

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1600

Maple

revdigs:= proc(x) local F, i;
  F:= convert(x, base, 10);
  add(F[-i]*10^(i-1), i=1..nops(F))
end proc:
f1:= proc(n)
  local m0,  a0, b0, m, a, b, c, x;
  m0:= ilog10(n)+1;
  if m0::even then m:= m0/2+1; a0:= 1; b0:= 0;
  else a0:= floor(n/10^(m0-1));
       if a0 = 4 or a0 = 5 then a0:= 7; b0:= 0
       elif a0::odd then b0:= n - 10^(m0-1)*a0;
     else a0:= a0+1; b0:= 0;
     fi;
     m:= ceil(m0/2); b0:= floor(b0/10^(m-1));
  fi;
  for a from a0 to 9 by 2 do
    for b from b0 to 10^(m-1)  do
      x:= 10^(m-1)*a + b;
      x:= 10^(m-1)*x + revdigs(floor(x/10));
      if x < n then next fi;
      if isprime(x) then return x fi
    od;
    b0:= 0;
 od;
 procname(10^m0);
end proc;
A[1]:= 2: A[2]:= 5: A[3]:= 11:
for n from 4 to 30 do
   A[n]:= f1(2*A[n-1]-A[n-2]+1);
od:
seq(A[i], i=1..30); # Robert Israel, Jan 31 2019

Mathematica

p = 1; d = 0; Do[ q = FromDigits[ Join[ IntegerDigits[n], Drop[ Reverse[ IntegerDigits[n]], 1]]]; If[ PrimeQ[q] && q - p > d, Print[q]; d = q - p; p = q], {n, 2, 3000002}]

Crossrefs

Cf. A071250.

Sequence in context: A178318 A134996 A134998 * A158999 A283300 A069506

Adjacent sequences: A078787 A078788 A078789 * A078791 A078792 A078793

Keyword

base,nonn

Author

Robert G. Wilson v, Dec 03 2002

Extensions

Corrected by T. D. Noe, Oct 25 2006

Corrected and more terms from Robert Israel, Jan 31 2019

Status

approved