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.

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A105268 Primes which are 1 + strobogrammatic numbers A000787(n): the same upside down.

Original entry on oeis.org

2, 89, 97, 809, 907, 8009, 8699, 9697, 9887, 81119, 98887, 8000009, 9888887, 81111119, 8111111119, 8666699999, 9888888887, 8000000000009, 9888888888887, 98888888888888887, 81111111111111111119, 800000000000000000009
Offset: 1

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Author

Jonathan Vos Post, Apr 16 2005

Keywords

Comments

Primes which, upon subtracting one, give numbers which read the same upside-down. Not to be confused with strobogrammatic primes A007597 such as 181 or 619. Also, 263 is the largest known prime whose square is strobogrammatic. Not to be confused with strobogrammatic squares A018848 such as 109181601. After a(7) this sequence is exemplary, not complete (i.e. missing some values).

Examples

			9887 is prime, 9887 = 9886+1 and 9886 turned upside-down is 9886 again.

Crossrefs

Cf. A000040, A000787, A007597, A018847, A018848.

Formula

{A000787(n)+1} intersect {A000040}.

Extensions

Term a(17) reordered by Georg Fischer, Mar 20 2022

A107465 Numbers k such that 10^k*(66161819199+10^(k+10)) + 1 is prime.

Original entry on oeis.org

3, 32, 96, 104, 603, 870, 1609, 2505, 4889, 5024, 5345, 14955
Offset: 1

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Author

Jason Earls, May 27 2005

Keywords

Comments

These are non-palindromic strobogrammatic primes and they have all been certified. No more terms up to 8700. Primality proof for the largest (a "gigantic" prime): PFGW Version 20041001.Win_Stable (v1.2 RC1b) [FFT v23.8] Primality testing 10^5345*(66161819199+10^(5345+10))+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 34.91% 10^5345*(66161819199+10^(5345+10))+1 is prime! (15.1367s+0.0109s)

Links

Crossrefs

Cf. A007597.

Programs

Extensions

a(12) from Michael S. Branicky, Sep 21 2024

A133030 Divisors of 5130.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 27, 30, 38, 45, 54, 57, 90, 95, 114, 135, 171, 190, 270, 285, 342, 513, 570, 855, 1026, 1710, 2565, 5130
Offset: 1

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Author

Omar E. Pol, Oct 27 2007

Keywords

Comments

5130 spells OEIS when turned upside down on a calculator: 57*90 = 5130 ---> OEIS.

Links

Crossrefs

Cf. A000787, A001840, A007597, A018278, A018365, A018846, A048889, A080789.

Programs

A155801 Nontrivial "Strobogrammatic" primes, the same "upside-down" in at least one base b with 2 <= b <= 10.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 31, 37, 43, 73, 101, 107, 127, 181, 257, 313, 443, 619, 757, 1093, 1193, 1297, 1453, 1571, 1619, 1787, 1831, 1879, 2801, 4889, 5113, 5189, 5557, 5869, 5981, 6211, 6827, 7607, 7759, 7919, 8191
Offset: 1

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Author

Jonathan Vos Post, Jan 27 2009

Keywords

Comments

I have to say "nontrivial" because every nonnegative integer is strobogrammatic in base 1. Strobogrammatic binary primes == primes in A006995 == A016041. Strobogrammatic primes in base 3 = 13, 757, 1093, 9103, ... == primes strobogrammatic in bases 2 and 3. For bases 2 < k < 8 we have that every strobogrammatic prime in base k must also be strobogrammatic in base 2 and hence palindromic in base 2. Hence we have, for example, strobogrammatic base-4 primes = A056130 = "Palindromic primes in bases 2 and 4."
Strobogrammatic primes in base 5 = 31, 19531, 394501, 472631, ... == primes strobogrammatic in base 2 and base 5. Strobogrammatic primes base 6 = 7, 37, 43, 1297, 55987, ... == primes strobogrammatic in base 2 and base 6. Note that 1101011 (base 6) = 18881 (base 10) which is strobogrammatic base 10 but not prime base 6 nor 10 (though prime base 2). Strobogrammatic primes base 7 = 2801, 134807, this last being strobogrammatic prime in bases 2, 4 and 7. Strobogrammatic primes base 8 = 73, 262657, 295433, ... Strobogrammatic primes base 9 break the above pattern, as they can have the digit 8 and are A068188 (tetradic primes). Strobogrammatic primes base 10 == A007597. Except sometimes for the first element, these (for the same range of k) must all have an odd number of digits.

Examples

			5189 = 1101011 (base 6) which numeral string is the same upside-down (and backwards). 11, 101, 181 and 619 are strobogrammatic base 10, the conventional interpretation of the word.

Crossrefs

Cf. A000040, A006995, A016041, A056130, A007597, A133207, A155584.

Formula

A000040 INTERSECTION A155584[1 < k < 11, n].

A287092 Strobogrammatic nonpalindromic numbers.

Original entry on oeis.org

69, 96, 609, 619, 689, 906, 916, 986, 1691, 1961, 6009, 6119, 6699, 6889, 6969, 8698, 8968, 9006, 9116, 9696, 9886, 9966, 16091, 16191, 16891, 19061, 19161, 19861, 60009, 60109, 60809, 61019, 61119, 61819, 66099, 66199, 66899, 68089, 68189, 68889, 69069, 69169, 69869, 86098, 86198, 86898, 89068, 89168
Offset: 1

Views

Author

Ilya Gutkovskiy, May 19 2017

Keywords

Comments

Nonpalindromic numbers which are invariant under a 180-degree rotation.
Numbers that are the same upside down and containing digits 6, 9.
Intersection of A000787 and A029742.
Union of this sequence and A006072 gives A000787.

Crossrefs

Cf. A000787, A007597, A018848, A029742, A006072, A153806, A169731.

Programs

  • Mathematica
    fQ[n_] := Block[{s = {0, 1, 6, 8, 9}, id = IntegerDigits[n]}, If[ Union[ Join[s, id]] == s && (id /. {6 -> 9, 9 -> 6}) == Reverse[id], True, False]]; Select[ Range[0, 89168], fQ[ # ] && ! PalindromeQ[ # ] &]
Previous Showing 11-15 of 15 results.

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

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