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A134971
Canyon primes.
9
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
1,1
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.
LINKS
FORMULA
A000040 INTERSECT A134970.
EXAMPLE
Illustration of 751367 as a Canyon prime:
. . . . . .
. . . . . .
7 . . . . 7
. . . . 6 .
. 5 . . . .
. . . . . .
. . . 3 . .
. . . . . .
. . 1 . . .
. . . . . .
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 *)
PROG
(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
CROSSREFS
Cf. A000040, A134951, Primes in A134970.
Sequence in context: A256048 A252942 A090287 * A082770 A161907 A195855
KEYWORD
nonn,base,fini,full
AUTHOR
Omar E. Pol, Nov 25 2007
EXTENSIONS
All terms past 3203, more comments, etc. by Kellen Myers, Jan 18 2011
STATUS
approved