A134971 Canyon primes.

101, 313, 727, 757, 919, 929, 3023, 3203, 7027, 7057, 7127, 7207, 7237, 7247, 7307, 7417, 7457, 7507, 7517, 7537, 7547, 7607, 9029, 9049, 9059, 9109, 9209, 9239, 9319, 9349, 9419, 9439, 9479, 9539, 9619, 9629, 9649, 9679, 9689, 9719, 9739, 9749, 9769, 9829

Offset: 1

Author

Omar E. Pol, Nov 25 2007

Keywords

• nonn
• base
• fini
• full

Comments

Intersection of prime numbers and Canyon numbers ("Canyon primes"). This sequence is finite because A134970 is. There are 9237 Canyon primes (compare to 116505 Canyon numbers total). The largest Canyon prime (and last element of this sequence) is a(9237) = 98765432101456789.

Examples

			Illustration of 751367 as a Canyon prime:
. . . . . .
. . . . . .
7 . . . . 7
. . . . 6 .
. 5 . . . .
. . . . . .
. . . 3 . .
. . . . . .
. . 1 . . .
. . . . . .
		

Links

• Kellen Myers, Table of n, a(n) for n = 1..9237

Crossrefs

Cf. A000040, A134951, Primes in A134970.

Programs

Mathematica

S = {}; c = 1;
For[n = 1, n <= 9, n++,
  L = 2 n - 1;
  d = Join[Reverse[Range[1, n - 1]], Range[0, n - 1]];
  If[Mod[n, 2] != 0 && n != 5,
   For[j = 1, j < 2^L, j++,
     Dig = d[[Map[#[[1]] &, Position[IntegerDigits[j, 2, L], 1]]]];
     min = Min[Dig];
     If[Length[Position[Dig, min]] == 1,
      p = FromDigits[Join[{n}, Dig, {n}]];
      If[PrimeQ[p], S = Append[S, p]];
      ];
     ];
   ];
  ]; (* Kellen Myers, Jan 18 2011 *)

Python

from sympy import isprime
from itertools import chain, combinations as combs
ups = list(chain.from_iterable(combs(range(10), r) for r in range(2, 11)))
s = set(L[::-1] + R[1:] for L in ups for R in ups if L[0] == R[0])
afull = sorted(filter(isprime, (int("".join(map(str, t))) for t in s if t[0] == t[-1])))
print(afull[:44]) # Michael S. Branicky, Jan 16 2023

Formula

A000040 INTERSECT A134970.

Extensions

All terms past 3203, more comments, etc. by Kellen Myers, Jan 18 2011