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.

Showing 1-5 of 5 results.

A057708 Numbers m such that 2^m reversed is prime.

Original entry on oeis.org

1, 4, 5, 7, 10, 17, 24, 37, 45, 55, 70, 77, 107, 137, 150, 271, 364, 1157, 1656, 2004, 2126, 3033, 3489, 3645, 4336, 6597, 7279, 12690, 13840, 20108, 21693, 28888, 84155, 102930
Offset: 1

Views

Author

G. L. Honaker, Jr., Oct 23 2000

Keywords

Comments

a(35) > 105000. - Giovanni Resta, Feb 22 2013
From Bernard Schott, Jan 30 2022: (Start)
If m is an even term, then u = m/2 is a term of A350441, this because 2^m = 4^(m/2). In fact, terms of A350441 are half the even terms of this sequence here.
If m is a term multiple of 3, then k = m/3 is a term of A350442, this because 2^m = 8^(m/3). First examples: m = 24, 45, 150, 1656, ... and corresponding k = 8, 15, 50, 552, ... (End)
a(35) > 200000. - Michael S. Branicky, May 12 2025

Examples

			4 is a term because 2^4 reversed is 61 and prime.

Crossrefs

Cf. A004094, A341713.
Numbers m such that k^m reversed is prime: this sequence (k=2), A350441 (k=4), A058993 (k=5), A058994 (k=7), A350442 (k=8), A058995 (k=13).

Programs

  • Maple
    with(numtheory): myarray := []: for n from 1 to 4000 do it1 := convert(2^n, base, 10): it2 := sum(10^(nops(it1)-i)*it1[i], i=1..nops(it1)): if isprime(it2) then printf(`%d,`,n) fi: od:
  • Mathematica
    Do[ If[ PrimeQ[ FromDigits[ Reverse[ IntegerDigits[2^n]] ]], Print[ n]], {n, 20000}] (* Robert G. Wilson v, Jan 29 2005 *)
Select[Range[4400],PrimeQ[IntegerReverse[2^#]]&] (* Requires Mathematica version 10 or later *) (* The program generates the first 25 terms of the sequence; to generate more, increase the Range constant, but the program will take longer to run. *) (* Harvey P. Dale, Aug 05 2020 *)
  • PARI
    isok(m) = isprime(fromdigits(Vecrev(digits(2^m)))) \\ Mohammed Yaseen, Jul 20 2022
  • Python
    from sympy import isprime
k, m, A057708_list = 1, 2,  []
while k <= 10**3:
    if isprime(int(str(m)[::-1])):
        A057708_list.append(k)
    k += 1
    m *= 2 # Chai Wah Wu, Mar 09 2021

Extensions

More terms from Chris Nash (chris_nash(AT)prodigy.net), Oct 25 2000
Two more terms from Robert G. Wilson v, Jan 29 2001
3 more terms from Farideh Firoozbakht, Aug 05 2004
a(33)-a(34) from Giovanni Resta, Feb 22 2013

A058993 Numbers m such that 5^m reversed is a prime.

Original entry on oeis.org

1, 3, 26, 36, 43, 66, 76, 149, 511, 885, 3767, 18157, 20516, 26316
Offset: 1

Views

Author

Robert G. Wilson v, Jan 17 2001

Keywords

Crossrefs

Cf. A059206, A071583.
Numbers m such that k^m reversed is prime: A057708 (k=2), A350441 (k=4), this sequence (k=5), A058994 (k=7), A350442 (k=8), A058995 (k=13).

Programs

  • Mathematica
    Do[ If[ PrimeQ[ ToExpression[ StringReverse[ ToString[5^n] ] ] ], Print[n] ], {n, 1, 3000} ]
  • PARI
    isok(m) = isprime(fromdigits(Vecrev(digits(5^m)))) \\ Mohammed Yaseen, Jul 20 2022
  • Python
    from sympy import isprime
k, m, A058993_list = 1, 5,  []
while k <= 10**3:
    if isprime(int(str(m)[::-1])):
        A058993_list.append(k)
    k += 1
    m *= 5 # Chai Wah Wu, Mar 09 2021

Extensions

a(12)-a(14) from Michael S. Branicky, Apr 01 2023

A058994 Numbers m such that 7^m reversed is prime.

Original entry on oeis.org

1, 12, 24, 225, 392, 819, 1201, 1645, 1775, 37578
Offset: 1

Views

Author

Robert G. Wilson v, Jan 17 2001

Keywords

Crossrefs

Cf. A059208, A071584.
Numbers m such that k^m reversed is prime: A057708 (k=2), A350441 (k=4), A058993 (k=5), this sequence (k=7), A350442 (k=8), A058995 (k=13).

Programs

  • Mathematica
    Do[ If[ PrimeQ[ ToExpression[ StringReverse[ ToString[7^n] ] ] ], Print[n] ], {n, 1, 2500} ]
  • PARI
    isok(m) = isprime(fromdigits(Vecrev(digits(7^m)))) \\ Mohammed Yaseen, Jul 20 2022
  • Python
    from sympy import isprime
k, m, A058994_list = 1, 7,  []
while k <= 10**3:
    if isprime(int(str(m)[::-1])):
        A058994_list.append(k)
    k += 1
    m *= 7 # Chai Wah Wu, Mar 09 2021

Extensions

a(10) from Michael S. Branicky, Mar 16 2025

A350441 Numbers m such that 4^m reversed is prime.

Original entry on oeis.org

2, 5, 12, 35, 75, 182, 828, 1002, 1063, 2168, 6345, 6920, 10054, 14444, 51465
Offset: 1

Views

Author

Mohammed Yaseen, Dec 31 2021

Keywords

Comments

From Bernard Schott, Jan 30 2022: (Start)
If m is a term, then u = 2*m is a term of A057708, because 4^m = 2^(2*m). In fact, terms of this sequence here are half the even terms of A057708.
If m is a term that is multiple of 3, then k = 2*m/3 is a term of A350442, because 4^m = 8^(2m/3). First examples: m = 12, 75, 828, 1002, 6345, 51465, ... and corresponding k = 8, 50, 552, 668, 4230, 34310, ... (End)

Crossrefs

Cf. A058996, A071582.
Cf. Numbers m such that k^m reversed is prime: A057708 (k=2), this sequence (k=4), A058993 (k=5), A058994 (k=7), A350442 (k=8), A058995 (k=13).

Programs

  • Mathematica
    Select[Range[2200], PrimeQ[IntegerReverse[4^#]] &] (* Amiram Eldar, Dec 31 2021 *)
  • PARI
    isok(m) = isprime(fromdigits(Vecrev(digits(4^m))))
  • Python
    from sympy import isprime
m = 4
for n in range (1, 2000):
    if isprime(int(str(m)[::-1])):
        print(n)
    m *= 4

Extensions

a(11)-a(15) from Amiram Eldar, Dec 31 2021

A350442 Numbers m such that 8^m reversed is prime.

Original entry on oeis.org

8, 15, 50, 552, 668, 1011, 1163, 1215, 2199, 4230, 7231, 34310
Offset: 1

Views

Author

Mohammed Yaseen, Dec 31 2021

Keywords

Comments

From Bernard Schott, Jan 30 2022: (Start)
If k is a term, then u = 3*k is a term of A057708, because 8^k = 2^(3k).
If k is an even term, then t = 3*k/2 is a term of A350441, because 8^k = 4^(3k/2). First examples: k = 8, 50, 552, 668, 4230, 34310, ... and corresponding t = 12, 75, 828, 1002, 6345, 51465, ... (End)

Crossrefs

Cf. A059003, A071586.
Cf. Numbers m such that k^m reversed is prime: A057708 (k=2), A350441 (k=4), A058993 (k=5), A058994 (k=7), A058995 (k=13).

Programs

  • Mathematica
    Select[Range[2200], PrimeQ[IntegerReverse[8^#]] &] (* Amiram Eldar, Dec 31 2021 *)
  • PARI
    isok(m) = isprime(fromdigits(Vecrev(digits(8^m))))
  • Python
    from sympy import isprime
m = 8
for n in range (1, 2000):
    if isprime(int(str(m)[::-1])):
        print(n)
    m *= 8

Extensions

a(10)-a(12) from Amiram Eldar, Dec 31 2021
Showing 1-5 of 5 results.

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

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