A134811 -id:A134811 - cp's OEIS frontend

A167844 Convex primes.

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

A173071 Palindromic mountain primes.

Original entry on oeis.org

131, 151, 181, 191, 12421, 12721, 12821, 13831, 13931, 14741, 17971, 1235321, 1245421, 1257521, 1268621, 1278721, 1456541, 1469641, 1489841, 1579751, 1589851, 123484321, 123494321, 123575321, 136797631, 167898761, 12345854321

Offset: 1

Omar E. Pol, Feb 09 2010

All terms have an odd number of digits. - Emeric Deutsch, Mar 09 2010

			a(6) = 12721; is a palindromic mountain prime.
. . . . .
. . . . .
. . 7 . .
. . . . .
. . . . .
. . . . .
. . . . .
. 2 . 2 .
1 . . . 1

Chai Wah Wu, Table of n, a(n) for n = 1..39

Cf. A002113, A002385, A134810, A134811, A134941, A134951.

a := proc (n) local rev, n1: rev := proc (n) local nn: nn := convert(n, base, 10): add(nn[j]*10^(nops(nn)-j), j = 1 .. nops(nn)) end proc: n1 := convert(n, base, 10): if n1[1]=1 and isprime(n) = true and rev(n) = n and n1[1] < n1[2] and n1[2] < n1[3] and n1[3] < n1[4] then n else end if end proc: seq(a(n), n = 1000000 .. 9999999); # this program works only for 7-digit numbers; easily adjustable for other (2k+1)-digit numbers # Emeric Deutsch, Mar 09 2010

from itertools import combinations
from gmpy2 import is_prime
A173071_list = []
for l in range(1,10):
    for i in combinations('23456789',l):
        s = '1'+''.join(i)
        p = int(s+s[l-1::-1])
        if is_prime(p):
            A173071_list.append(p) # Chai Wah Wu, Nov 05 2015

More terms from Emeric Deutsch, Mar 09 2010, corrected Mar 19 2010

a(22)-a(27) from Donovan Johnson, Jul 22 2010

A244369 Palindromic right-angled primes.

Original entry on oeis.org

101, 787, 34543, 7654567, 345676543, 34567876543

Offset: 1

Omar E. Pol, Jun 26 2014

Intersection of A002113 and A167842.
Intersection of A002385 and A135602.
The last term of this sequence is also the last term of A134811.

			Illustration of a(6) = 34567876543, the last term of this sequence:
. . . . . . . . . . .
. . . . . 8 . . . . .
. . . . 7 . 7 . . . .
. . . 6 . . . 6 . . .
. . 5 . . . . . 5 . .
. 4 . . . . . . . 4 .
3 . . . . . . . . . 3
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .

Cf. A000040, A002113, A002385, A134811, A135602, A167842.

from sympy import isprime
A244369 = []
for n in range(1,10):
    for m in range(n-1,-1,-1):
        l = ''.join([str(d) for d in range(n,m-1,-1)])
        p = int(l+l[-2::-1])
        if isprime(p):
            A244369.append(p)
    for m in range(n+1,10):
        l = ''.join([str(d) for d in range(n,m+1)])
        p = int(l+l[-2::-1])
        if isprime(p):
            A244369.append(p)
A244369 = sorted(A244369) # Chai Wah Wu, Aug 15 2014

A182775 Giza nonprimes.

Original entry on oeis.org

1, 4, 6, 8, 9, 121, 232, 343, 454, 565, 676, 898, 12321, 23432, 45654, 56765, 67876, 78987, 1234321, 2345432, 3456543, 4567654, 5678765, 6789876, 123454321, 234565432, 456787654, 567898765, 12345654321, 23456765432, 45678987654

Offset: 1

Omar E. Pol, Dec 16 2010

I propose the name Giza nonprimes.

The total number of terms is 37. The largest is 12345678987654321 which is also the largest mountain number A134941.

			a(6)=121 is in the sequence because 121 is a nonprime number A018252 and 121 is also a Giza number A134810.
The last six terms of this finite sequence are
a(32) = 1234567654321
a(33) = 2345678765432
a(34) = 3456789876543
a(35) = 123456787654321
a(36) = 234567898765432
a(37) = 12345678987654321
Illustration of a(37) as a Giza nonprime:
. . . . . . . . 9 . . . . . . . .
. . . . . . . 8 . 8 . . . . . . .
. . . . . . 7 . . . 7 . . . . . .
. . . . . 6 . . . . . 6 . . . . .
. . . . 5 . . . . . . . 5 . . . .
. . . 4 . . . . . . . . . 4 . . .
. . 3 . . . . . . . . . . . 3 . .
. 2 . . . . . . . . . . . . . 2 .
1 . . . . . . . . . . . . . . . 1

Cf. A018252, A134810, A134811, A134941, A182776.

Select[Union[FromDigits/@Select[Flatten[Table[Table[Join[Range[i,i+n], Reverse[ Most[ Range[ i,i+n]]]],{n,0,9}],{i,9}],1],Max[#]<10&]], !PrimeQ[#]&] (* Harvey P. Dale, Aug 23 2011 *)

A018252 INTERSECT A134810.

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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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A173071 Palindromic mountain primes.

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A244369 Palindromic right-angled primes.

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A182775 Giza nonprimes.

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