cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-15 of 15 results.

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

Views

Author

Omar E. Pol, Feb 09 2010

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

  • Maple
    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
  • Python
    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

Extensions

More terms from Emeric Deutsch, Mar 09 2010, corrected Mar 19 2010
a(22)-a(27) from Donovan Johnson, Jul 22 2010

A173070 Palindromic mountain numbers.

Original entry on oeis.org

1, 121, 131, 141, 151, 161, 171, 181, 191, 12321, 12421, 12521, 12621, 12721, 12821, 12921, 13431, 13531, 13631, 13731, 13831, 13931, 14541, 14641, 14741, 14841, 14941, 15651, 15751, 15851, 15951, 16761, 16861, 16961, 17871, 17971, 18981
Offset: 1

Views

Author

Omar E. Pol, Feb 09 2010

Keywords

Comments

There are 256 terms, the last of which is 12345678987654321. - Michael S. Branicky, Aug 04 2022

Examples

			13731 is in the sequence because it is a palindrome (A002113) and it is also a mountain number (A134941).
. . . . .
. . . . .
. . 7 . .
. . . . .
. . . . .
. . . . .
. 3 . 3 .
. . . . .
1 . . . 1

Links

Crossrefs

Cf. A002113, A134941, A134951, A134810, A134853, A173071

Programs

  • Python
    from itertools import chain, combinations as combs
def c(s): return s[0] == s[-1] == 1 and s == s[::-1]
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[-1] == R[-1])
afull = [1] + sorted(int("".join(map(str, t))) for t in s if c(t))
print(afull[:40]) # Michael S. Branicky, Aug 04 2022

A182721 Mountain emirps.

Original entry on oeis.org

1231, 1321, 1381, 1471, 1741, 1831, 12491, 12641, 12841, 13591, 13751, 13781, 13841, 14591, 14621, 14821, 14831, 14891, 15731, 15791, 18731, 19421, 19531, 19541, 19751, 19841, 123731, 123821, 124951, 124981, 125641, 125651, 125791, 125821, 125941, 126761, 126851
Offset: 1

Views

Author

Omar E. Pol, Dec 21 2010

Keywords

Comments

Intersection of emirps A006567 and mountain numbers A134941.
The smallest mountain emirp 1231 and other terms of this sequence was mentioned by Loungrides in Prime Curios! (see link).
Question: How many are there?
There are 602 such terms. - Michael S. Branicky, Dec 31 2021

Examples

			Illustration of a(11) = 13751 as a mountain emirp:
  . . . . .
  . . . . .
  . . 7 . .
  . . . . .
  . . . 5 .
  . . . . .
  . 3 . . .
  . . . . .
  1 . . . 1

Links

Crossrefs

Cf. A006567, A134941, A134951, A135417, A173071.

Programs

  • Python
    # uses A134941()
from sympy import isprime
def is_emirp(n):
    if not isprime(n): return False
    revn = int(str(n)[::-1])
    return n != revn and isprime(revn)
print([k for k in A134941() if is_emirp(k)]) # Michael S. Branicky, Dec 31 2021

Formula

A006567 INTERSECT A134941.

Extensions

More terms from Nathaniel Johnston, Dec 29 2010
Terms a(31) and beyond from Michael S. Branicky, Dec 31 2021

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

Original entry on oeis.org

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

Views

Author

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

Keywords

Comments

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

References

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

Links

Crossrefs

Cf. A000040, A134951, A134971.

Extensions

Edited by N. J. A. Sloane, Jan 09 2011
Extended by D. S. McNeil, Jan 09 2011

A182776 Mountain nonprimes.

Original entry on oeis.org

1, 121, 141, 161, 171, 1241, 1251, 1261, 1271, 1281, 1341, 1351, 1371, 1391, 1421, 1431, 1461, 1491, 1521, 1541, 1561, 1581, 1591, 1631, 1641, 1651, 1671, 1681, 1691, 1731, 1751, 1761, 1781, 1791, 1821, 1841, 1851, 1891, 1921, 1941, 1961, 1971, 1981, 12321, 12341, 12351, 12361, 12371
Offset: 1

Views

Author

Omar E. Pol, Dec 14 2010

Keywords

Comments

The total number of terms is 19226. The largest is 12345678987654321 which is also the largest Giza number A134810.

Examples

			a(2)=121 is in the sequence because 121 is a nonprime number A018252 and 121 is also a mountain number A134941.
Illustration of 134961 as a mountain nonprime:
. . . 9 . .
. . . . . .
. . . . . .
. . . . 6 .
. . . . . .
. . 4 . . .
. 3 . . . .
. . . . . .
1 . . . . 1

Crossrefs

Cf. A018252, A134810, A134941, A134951.

Formula

A018252 INTERSECT A134941.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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