A183087 Generalized canyon primes.

101, 103, 107, 109, 307, 313, 317, 401, 409, 419, 439, 503, 509, 523, 547, 601, 607, 613, 617, 619, 647, 659, 701, 709, 719, 727, 739, 757, 769, 809, 823, 827, 829, 839, 857, 859, 907, 919, 929, 937, 947, 967, 1013, 1019, 1039, 1049, 1069, 2017, 2027, 2029

Offset

1,1

Comments

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.

This sequence is finite because A183086 is.

Questions: How many terms are there in this sequence?

What is the largest term?

There are 24356 terms, the largest of which is 98765432101456789. - Michael S. Branicky, Aug 04 2022

Links

Michael S. Branicky, Table of n, a(n) for n = 1..24356 (full sequence)

Formula

A000040 INTERSECT A183086.

Example

Illustration of 751379 as a generalized canyon prime:
. . . . . 9
. . . . . .
7 . . . 7 .
. . . . . .
. 5 . . . .
. . . . . .
. . . 3 . .
. . . . . .
. . 1 . . .
. . . . . .

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)))
print(afull[:50]) # Michael S. Branicky, Aug 04 2022

Crossrefs

Cf. A134971, A167853, A183086.

Sequence in context: A048528 A164739 A085821 * A056709 A243825 A345728

Adjacent sequences: A183084 A183085 A183086 * A183088 A183089 A183090

Keyword

nonn,base,fini,full

Author

Omar E. Pol, Jan 19 2011

Extensions

Missing 601 inserted by Michael S. Branicky, Aug 04 2022

Status

approved