A007500 -id:A007500 - cp's OEIS frontend

A075235 Primes whose base 5 reversal is also prime.

2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 149, 151, 157, 163, 167, 191, 193, 211, 223, 227, 229, 233, 239, 251, 257, 269, 271, 277, 281, 293, 317, 331, 337, 347, 349, 353, 359, 367

Offset: 1

Robert G. Wilson v, Sep 09 2002

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007500, A074832, A074833, A074834, A075236, A075237, A075238, A075239.

Prime[ Select[ Range[100], PrimeQ[ FromDigits[ Reverse[ IntegerDigits[ Prime[ # ], 5]], 5]] &]]

A075236 Primes whose base 6 reversal is also prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 37, 41, 43, 53, 59, 61, 67, 71, 181, 191, 193, 197, 199, 211, 227, 233, 257, 263, 271, 277, 281, 293, 307, 311, 313, 317, 331, 337, 349, 359, 367, 373, 379, 383, 389, 431, 1087, 1093, 1103, 1109, 1117, 1123, 1153, 1187, 1193, 1201, 1213

Offset: 1

Robert G. Wilson v, Sep 09 2002

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007500, A074832, A074833, A074834, A075235, A075237, A075238, A075239.

Prime[ Select[ Range[200], PrimeQ[ FromDigits[ Reverse[ IntegerDigits[ Prime[ # ], 6]], 6]] &]]
Select[Prime[Range[200]],PrimeQ[FromDigits[Reverse[IntegerDigits[#,6]],6]]&] (* Harvey P. Dale, Oct 12 2023 *)

A075237 Primes whose base 7 reversal is also prime.

Original entry on oeis.org

2, 3, 5, 11, 13, 17, 19, 23, 29, 37, 41, 43, 47, 53, 67, 71, 79, 89, 97, 101, 107, 127, 137, 139, 149, 151, 157, 167, 173, 179, 193, 197, 199, 211, 227, 229, 233, 241, 257, 269, 271, 277, 281, 307, 311, 331, 337, 347, 373, 389, 397, 401, 419, 421, 433, 439, 443

Offset: 1

Robert G. Wilson v, Sep 09 2002

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007500, A074832, A074833, A074834, A075235, A075236, A075238, A075239.

Prime[ Select[ Range[100], PrimeQ[ FromDigits[ Reverse[ IntegerDigits[ Prime[ # ], 7]], 7]] &]]

A075238 Primes whose base 8 reversal is also prime.

Original entry on oeis.org

2, 3, 5, 7, 13, 29, 31, 41, 43, 47, 59, 61, 67, 71, 73, 79, 89, 97, 101, 107, 113, 193, 211, 227, 233, 239, 251, 349, 353, 373, 383, 449, 457, 463, 479, 487, 491, 503, 509, 521, 523, 541, 577, 587, 643, 677, 683, 719, 733, 751, 757, 773, 787, 811, 823, 827, 829

Offset: 1

Robert G. Wilson v, Sep 09 2002

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Cf. A007500, A074832, A074833, A074834, A075235, A075236, A075237, A075239.

Prime[ Select[ Range[150], PrimeQ[ FromDigits[ Reverse[ IntegerDigits[ Prime[ # ], 8]], 8]] &]]
Select[Prime[Range[200]],PrimeQ[IntegerReverse[#,8]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 09 2017 *)

A075239 Primes whose base 9 reversal is also prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 37, 43, 47, 67, 71, 73, 79, 83, 97, 101, 109, 113, 127, 139, 151, 157, 163, 173, 179, 181, 191, 193, 197, 227, 229, 239, 241, 331, 337, 353, 367, 373, 379, 383, 389, 397, 419, 433, 439, 457, 463, 479, 571, 577, 593, 599, 601, 607

Offset: 1

Robert G. Wilson v, Sep 09 2002

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007500, A074832, A074833, A074834, A075235, A075236, A075237, A075238.

Prime[ Select[ Range[115], PrimeQ[ FromDigits[ Reverse[ IntegerDigits[ Prime[ # ], 9]], 9]] &]]

A076056 Primes which when read backwards are composite numbers.

Original entry on oeis.org

19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 103, 109, 127, 137, 139, 163, 173, 193, 197, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 317, 331, 349, 367, 379, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457

Offset: 1

Amarnath Murthy, Oct 04 2002

Subsidiary sequences that could be added:(1) Start of the first occurrence of n consecutive primes in the above sequence. (2) Start of the first occurrence of n consecutive primes with digit reversal also a prime.
The subsidiary sequence (1) with the indices at which n>=2 consecutive primes are first found in this sequence is 1, 1, 4, 4, 4, 4, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, ... - R. J. Mathar, May 22 2009
Subsequence of A151768. - Reinhard Zumkeller, Jul 06 2009

Anders Hellström, Table of n, a(n) for n = 1..10000
Anders Hellström, Sage program

Cf. A076055.

Complement of A007500 with respect to A000040. [From Reinhard Zumkeller, Jul 06 2009]

[p: p in PrimesUpTo(500)|not IsPrime(Seqint(Reverse(Intseq(p))))]; // Vincenzo Librandi, Jun 03 2019

Select[Prime[Range[100]], !PrimeQ[FromDigits[Reverse[IntegerDigits[ # ]]]]&]

More terms from Harvey P. Dale, Oct 11 2002

A238850 Right-truncatable reversible primes in base 10.

Original entry on oeis.org

2, 3, 5, 7, 31, 37, 71, 73, 79, 311, 313, 373, 733, 739, 797, 3733

Offset: 1

Stanislav Sykora, Mar 06 2014

In a general base b, a number qualifies as a member iff: (i) it is a prime, (ii) when its digits in base b are reversed, it is still a prime, and (iii) when, in base b, it has more than one digit and the least significant one is dropped, the remaining prefix has the same properties. This implies that any base-b prefix of such a number, no matter how many right-side digits are truncated, is still a right-truncatable reversible prime. Sequences of this type appear to be all finite (see A238854, A238855, and A238856, used as examples).
This particular sequence is for base b = 10.
See also A238854 for comments on a more general context.

			739 is a member because it is a prime and so is 937, as well as the pair (73, 37) and 7.

Stanislav Sykora, PARI/GP scripts for genetic threads, with code and comments.

In base 16: A238851, 100: A238852, 256: A238853.
In base n: A238854 (largest), A238855 (totals), A238856 (maximum digits), A238857 (m-digit counts).
Cf. A007500, A023107, A024770, A237600, A237601, A237602.

PARI
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See the link.
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A238851 Right-truncatable, reversible primes in base 16.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 53, 59, 61, 83, 89, 113, 179, 191, 211, 863, 947, 977, 983, 991, 1429, 1439, 1823, 3061, 3067, 3389, 15161, 15643, 15733, 15737, 15739, 15859, 23029, 48989, 48991, 251737, 251831, 253751, 368471, 4060019

Offset: 1

Stanislav Sykora, Mar 06 2014

See A238850 for definitions, and A238854 for comments on general context.

These numbers are fully right-truncatable and reversible primes in base 16 (but listed in decimal format). They are 40 in all.

			The largest such number (4060019) is in hex format 0x3DF373. It is a prime, so is 0x373FD3, and 0x3DF37 has again the same properties.

Stanislav Sykora, PARI/GP scripts for genetic threads, with code and comments.

Cf. All in base 10: A238850, 100: A238852, 256: A238853.
Cf. In base n: A238854 (largest), A238855 (totals), A238856 (maximum digits), A238857 (m-digit counts).
Cf. A007500, A023107, A024770, A237600, A237601, A237602.

PARI
```
See the link.
```

A069706 Primes with property that swapping first and last digits also gives a prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 101, 107, 113, 131, 149, 151, 157, 167, 179, 181, 191, 199, 311, 313, 337, 347, 353, 359, 373, 383, 389, 701, 709, 727, 733, 739, 743, 751, 757, 761, 769, 787, 797, 907, 919, 929, 937, 941, 953, 967, 971, 983, 991, 1009, 1013

Offset: 1

Amarnath Murthy, Apr 08 2002

This is not the same as A007500, "palindromic" primes.

			1049 and 9041 both are primes hence both are members.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A007500, A069707, A069708.

swapdigs:= proc(n) local d;
  d:= ilog10(n);
  n + ((n mod 10)-floor(n/10^d))*(10^d-1);
end proc:
select(isprime and isprime @ swapdigs, [2,seq(2*i+1,i=1..10^4)]); # Robert Israel, Nov 11 2015

Do[t = IntegerDigits[ Prime[n]]; u = t; u[[1]] = t[[ -1]]; u[[ -1]] = t[[1]]; t = FromDigits[u]; If[ PrimeQ[t], Print[ Prime[n]]], {n, 1, 300}]

from sympy import prime, isprime
A069706_list = [2,3,5,7]
for i in range(5,10**6):
    p = prime(i)
    s = str(p)
    if isprime(int(s[-1]+s[1:-1]+s[0])):
        A069706_list.append(p) # Chai Wah Wu, Nov 11 2015

Edited and extended by Robert G. Wilson v, Apr 12 2002

Edited by N. J. A. Sloane, Jan 20 2009

A085298 a(n) is the smallest exponent x such that prime(n)^x when reversed is a prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 8, 7, 1, 1, 2, 5, 15, 10, 12, 4, 39, 1, 1, 1, 11, 2, 1, 1, 10, 1, 23, 1, 5, 1, 243, 2, 1, 1, 1, 23, 1, 34, 1, 1, 1, 2, 58, 1, 3, 9, 166, 17, 68, 8, 8, 3, 7, 5, 5, 2, 2, 2, 61, 11, 97, 1, 1, 10, 2, 1, 1, 41, 1, 1, 66, 1, 5, 1, 1, 2, 2, 8, 40, 2, 8, 19, 2, 2, 723

Offset: 1

Labos Elemer, Jun 24 2003

It is conjectured that for every n such exponent exists.

			a(n)=1 means that rev(prime(n)) is prime i.e. prime(n) is in A007500;
a(n)=2 means that rev(prime(n)^2) is prime but rev(prime(n)) is not, like n=8:p=19 and 91 is not a prime but rev[19^2]=rev[361]=163 is a prime;
For n, the first k exponent providing rev(prime(n)^k) prime can be quite large, like at n=87: rev(p(87)^723)=rev(449^723) is the first [probably] prime has 1918 decimal digits: 948......573.

Giovanni Resta, Table of n, a(n) for n = 1..100

Cf. A000040, A057708, A058993, A056994, A059695, A003459, A007500, A055387, A061461, A068652.

a:= proc(n) local k, p; p:= ithprime(n); for k while not isprime((s->
      parse(cat(seq(s[-i], i=1..length(s)))))(""||(p^k))) do od; k
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Sep 04 2019

a[n_] := Block[{k = 1}, While[! PrimeQ@ FromDigits@ Reverse@ IntegerDigits[ Prime[n]^k], k++]; k]; Array[a, 87] (* Giovanni Resta, Sep 04 2019 *)

a(n) = {my(x=1, p=prime(n)); while (!ispseudoprime(fromdigits(Vecrev(digits(p^x)))), x++); x;} \\ Michel Marcus, Sep 04 2019

a(n) = Min{x; reversed(prime(n)^x) is a prime}.

cp's OEIS Frontend

A075235 Primes whose base 5 reversal is also prime.

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Mathematica

A075236 Primes whose base 6 reversal is also prime.

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A075237 Primes whose base 7 reversal is also prime.

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Mathematica

A075238 Primes whose base 8 reversal is also prime.

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Mathematica

A075239 Primes whose base 9 reversal is also prime.

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Mathematica

A076056 Primes which when read backwards are composite numbers.

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Magma

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A238850 Right-truncatable reversible primes in base 10.

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PARI

A238851 Right-truncatable, reversible primes in base 16.

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PARI

A069706 Primes with property that swapping first and last digits also gives a prime.

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