cp's OEIS Frontend

A183087 Generalized canyon primes.

%I A183087 #14 Aug 04 2022 11:00:40
%S A183087 101,103,107,109,307,313,317,401,409,419,439,503,509,523,547,601,607,
%T A183087 613,617,619,647,659,701,709,719,727,739,757,769,809,823,827,829,839,
%U A183087 857,859,907,919,929,937,947,967,1013,1019,1039,1049,1069,2017,2027,2029
%N A183087 Generalized canyon primes.
%C A183087 Primes in A183086. Supersequence of A134971 because the restriction that both cliffs are at same level (first digit equal to the final digit) is dropped here.
%C A183087 This sequence is finite because A183086 is.
%C A183087 Questions: How many terms are there in this sequence?
%C A183087 What is the largest term?
%C A183087 There are 24356 terms, the largest of which is 98765432101456789. - _Michael S. Branicky_, Aug 04 2022
%H A183087 Michael S. Branicky, <a href="/A183087/b183087.txt">Table of n, a(n) for n = 1..24356</a> (full sequence)
%F A183087 A000040 INTERSECT A183086.
%e A183087 Illustration of 751379 as a generalized canyon prime:
%e A183087 . . . . . 9
%e A183087 . . . . . .
%e A183087 7 . . . 7 .
%e A183087 . . . . . .
%e A183087 . 5 . . . .
%e A183087 . . . . . .
%e A183087 . . . 3 . .
%e A183087 . . . . . .
%e A183087 . . 1 . . .
%e A183087 . . . . . .
%o A183087 (Python)
%o A183087 from sympy import isprime
%o A183087 from itertools import chain, combinations as combs
%o A183087 ups = list(chain.from_iterable(combs(range(10), r) for r in range(2, 11)))
%o A183087 s = set(L[::-1] + R[1:] for L in ups for R in ups if L[0] == R[0])
%o A183087 afull = sorted(filter(isprime, (int("".join(map(str, t))) for t in s)))
%o A183087 print(afull[:50]) # _Michael S. Branicky_, Aug 04 2022
%Y A183087 Cf. A134971, A167853, A183086.
%K A183087 nonn,base,fini,full
%O A183087 1,1
%A A183087 _Omar E. Pol_, Jan 19 2011
%E A183087 Missing 601 inserted by _Michael S. Branicky_, Aug 04 2022