A134971 -id:A134971 - cp's OEIS frontend

A179673 Canyon primes (A134971) whose first and last digits are 9.

919, 929, 9029, 9049, 9059, 9109, 9209, 9239, 9319, 9349, 9419, 9439, 9479, 9539, 9619, 9629, 9649, 9679, 9689, 9719, 9739, 9749, 9769, 9829, 9839, 9859, 90149, 90239, 90289, 90359, 90379, 90469, 90679, 91019, 91079, 91249, 91369, 91459

Offset: 1

G. L. Honaker, Jr., Jan 08 2011

98765432101456789 is the largest term and the last element of this sequence.

Proposed by Charalambos Loungrides (loungrides(at)cytanet.cy)

Charles R Greathouse IV, Table of n, a(n) for n = 1..8480
Prime Curios, 98765432101456789

Cf. A000040, A134951, A134971.

Edited by N. J. A. Sloane, Jan 09 2011

Extended by D. S. McNeil, Jan 09 2011

A134970 Canyon numbers. Numbers with exactly one locally minimal digit and with exactly two locally maximal digits which are the same digit and nonadjacent.

Original entry on oeis.org

101, 202, 212, 303, 313, 323, 404, 414, 424, 434, 505, 515, 525, 535, 545, 606, 616, 626, 636, 646, 656, 707, 717, 727, 737, 747, 757, 767, 808, 818, 828, 838, 848, 858, 868, 878, 909, 919, 929, 939, 949, 959, 969, 979, 989, 2012, 2102, 3013, 3023

Offset: 1

Omar E. Pol, Nov 25 2007, Nov 26 2007

A digit of a number is a local minimum if it is less than (or equal to) its neighboring digit(s). It is a local maximum likewise if it is greater than (or equal to) its neighboring digit(s). For example, 55432123 has three local maxima (the two 5s and the end 3) and one local minimum (the 1).
Because they are nonadjacent, the maxima occur at the end (and the minimum somewhere between), and the sequence of digits must be decreasing up to the minimum, then increasing. This may be taken as part of the definition (which entails nonadjacency of the maxima).
The structure of digits represents a canyon (a deep valley between cliffs). The first digit is equal to the last digit. The first group of digits are in decreasing order. The second group of digits are in increasing order. The digits have a unique smallest digit which represents the bottom of the canyon.
This sequence is finite -- it has 116505 terms. The largest and final term of the sequence is a(116505) = 9876543210123456789.
9752369 is a canyon number because the unique minimum digit is the 2, and the maximum digit is 9 (at the beginning and end).

			Illustration of 4104 as a canyon number:
  4 . . 4
  . . . .
  . . . .
  . 1 . .
  . . 0 .

Kellen Myers, Table of n, a(n) for n = 1..116505

Cf. A134971.

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(int("".join(map(str, t))) for t in s if t[0] == t[-1])
print(afull[:60]) # Michael S. Branicky, Aug 02 2022

Edited by Kellen Myers, Jan 18 2011

A167844 Convex primes.

Original entry on oeis.org

101, 103, 107, 109, 113, 127, 137, 139, 149, 211, 223, 227, 229, 239, 307, 311, 313, 317, 337, 347, 349, 359, 401, 409, 419, 421, 433, 439, 449, 457, 503, 509, 521, 523, 547, 557, 569, 601, 607, 613, 617, 619, 631, 643, 647, 659, 701, 709, 719, 727, 733, 739

Offset: 1

Omar E. Pol, Nov 13 2009

Primes in A135641.
Primes whose structure of digits represents a convex function or a convex object. In the graphic representation the points are connected by imaginary line segments from left to right.
See A246033 for a different notion of "convex prime". - N. J. A. Sloane, Jul 25 2017

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A167844

Cf. A134811, A134951, A134971, A135641, A167841, A167842, A167843, A167845, A167846, A167853.

A167843 Obtuse-angled primes.

Original entry on oeis.org

113, 127, 137, 139, 149, 157, 167, 179, 199, 211, 223, 227, 229, 233, 239, 257, 269, 277, 311, 331, 337, 347, 349, 359, 367, 379, 389, 421, 431, 433, 443, 449, 457, 467, 479, 499, 521, 541, 557, 569, 577, 599, 631, 641, 643, 653, 661, 677, 733, 743, 751, 761

Offset: 1

Omar E. Pol, Nov 13 2009

Primes in A135603.

Primes whose structure of digits represents an obtuse angle. The vertex is an internal digit. In the graphic representation the points are connected by imaginary line segments from left to right.

Michael S. Branicky, Table of n, a(n) for n = 1..914

Cf. A134811, A134951, A134971, A135603, A167841, A167842, A167844, A167845, A167846, A167853.

# uses agen() from A135603
from sympy import isprime
g = filter(isprime, agen())
print([next(g) for n in range(1, 53)]) # Michael S. Branicky, Aug 03 2022

a(12) and beyond from Michael S. Branicky, Aug 03 2022

A167845 Concave primes.

Original entry on oeis.org

131, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 233, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 331, 353, 367, 373, 379, 383, 389, 397, 431, 443, 461, 463, 467, 479, 487, 491, 499, 541, 563, 571, 577, 587, 593, 599, 641, 653, 661, 673

Offset: 1

Omar E. Pol, Nov 13 2009

Primes in A135642.

Primes whose structure of digits represents a concave function or a concave object. In the graphic representation the points are connected by imaginary line segments from left to right.

Cf. A134811, A134951, A134971, A135642, A167841, A167842, A167843, A167844, A167846, A167853.

More terms from Max Alekseyev, Apr 24 2010

A167846 Concave-convex primes.

Original entry on oeis.org

1021, 1031, 1033, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423

Offset: 1

Omar E. Pol, Nov 13 2009

Primes in A163278.

Prime numbers with more than three digits that are not straight-line numbers (A135643), concave numbers (A135642) or convex numbers (A135641).

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A134811, A134951, A134971, A135641, A135642, A135643, A163278, A167841, A167842, A167843, A167844, A167845, A167853.

More terms from Rémy Sigrist, May 22 2019

A167847 Straight-line primes.

Original entry on oeis.org

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 4567, 76543, 23456789, 1111111111111111111, 11111111111111111111111

Offset: 1

Omar E. Pol, Nov 14 2009

Prime numbers with 2 digits together with the primes whose digits are in arithmetic progression. The structure of digits represents a straight line.
Note that in the graphic representation the points are connected by imaginary line segments (see also A135643).
Note that all two-digit primes are straight-line primes but this sequence has no three-digit terms.
No further terms between 23456789 and 115507867=prime(6600000). - R. J. Mathar, Dec 04 2009
All terms after 23456789 are repunit primes (A004022) with number of digits: 19, 23, 317, 1031, 49081, 86453, 109297, 270343, ... (A004023). - Jens Kruse Andersen, Jul 21 2014

			The number 4567 is straight-line prime:
  . . . .
  . . . .
  . . . 7
  . . 6 .
  . 5 . .
  4 . . .
  . . . .
  . . . .
  . . . .
  . . . .

Cf. A000040, A004022, A004023, A134811, A134951, A134971, A135643, A167841, A167842, A167843, A167844, A167845, A167846, A167853.

2 more terms from R. J. Mathar, Dec 04 2009

a(25)-a(26) from Jens Kruse Andersen, Jul 21 2014

A183087 Generalized canyon primes.

Original entry on oeis.org

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

Omar E. Pol, Jan 19 2011

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

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

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

Cf. A134971, A167853, A183086.

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

A000040 INTERSECT A183086.

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

cp's OEIS Frontend

A179673 Canyon primes (A134971) whose first and last digits are 9.

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A134970 Canyon numbers. Numbers with exactly one locally minimal digit and with exactly two locally maximal digits which are the same digit and nonadjacent.

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A167844 Convex primes.

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A167843 Obtuse-angled primes.

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A167845 Concave primes.

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A167846 Concave-convex primes.

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A167847 Straight-line primes.

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A183087 Generalized canyon primes.

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