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%I #38 Jan 16 2023 14:49:11
%S 101,313,727,757,919,929,3023,3203,7027,7057,7127,7207,7237,7247,7307,
%T 7417,7457,7507,7517,7537,7547,7607,9029,9049,9059,9109,9209,9239,
%U 9319,9349,9419,9439,9479,9539,9619,9629,9649,9679,9689,9719,9739,9749,9769,9829
%N Canyon primes.
%C 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.
%H Kellen Myers, <a href="/A134971/b134971.txt">Table of n, a(n) for n = 1..9237</a>
%F A000040 INTERSECT A134970.
%e Illustration of 751367 as a Canyon prime:
%e . . . . . .
%e . . . . . .
%e 7 . . . . 7
%e . . . . 6 .
%e . 5 . . . .
%e . . . . . .
%e . . . 3 . .
%e . . . . . .
%e . . 1 . . .
%e . . . . . .
%t S = {}; c = 1;
%t For[n = 1, n <= 9, n++,
%t L = 2 n - 1;
%t d = Join[Reverse[Range[1, n - 1]], Range[0, n - 1]];
%t If[Mod[n, 2] != 0 && n != 5,
%t For[j = 1, j < 2^L, j++,
%t Dig = d[[Map[#[[1]] &, Position[IntegerDigits[j, 2, L], 1]]]];
%t min = Min[Dig];
%t If[Length[Position[Dig, min]] == 1,
%t p = FromDigits[Join[{n}, Dig, {n}]];
%t If[PrimeQ[p], S = Append[S, p]];
%t ];
%t ];
%t ];
%t ]; (* _Kellen Myers_, Jan 18 2011 *)
%o (Python)
%o from sympy import isprime
%o from itertools import chain, combinations as combs
%o ups = list(chain.from_iterable(combs(range(10), r) for r in range(2, 11)))
%o s = set(L[::-1] + R[1:] for L in ups for R in ups if L[0] == R[0])
%o afull = sorted(filter(isprime, (int("".join(map(str, t))) for t in s if t[0] == t[-1])))
%o print(afull[:44]) # _Michael S. Branicky_, Jan 16 2023
%Y Cf. A000040, A134951, Primes in A134970.
%K nonn,base,fini,full
%O 1,1
%A _Omar E. Pol_, Nov 25 2007
%E All terms past 3203, more comments, etc. by _Kellen Myers_, Jan 18 2011
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