A007488 -id:A007488 - cp's OEIS frontend

A059002 Primes whose reversal is a seventh power.

821, 90367894271, 188372457491, 1938510215909, 67717549154641, 95168980930291, 772155318141637, 1558489460499871, 7505006230374799, 8237815094854781, 23021614989689299, 39712513595115047, 919042243755035867, 3573813286514042801, 7597919404531928707

Offset: 1

Robert G. Wilson v, Jan 16 2001

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007488.

rev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
S:= {}: count:= 0:
for d from 1 while count < 60 do
 for i from 10^(d-1) to 10^d do
  if i mod 10 = 0 then next fi;
  p:= rev(i^7);
  if isprime(p) then S:= S union {p}; count:= count+1; fi;
od od:
sort(convert(S,list)); # Robert Israel, Dec 22 2024

Do[ If[ PrimeQ[ n ] && IntegerQ[ ToExpression[ StringReverse[ ToString[ n ] ] ]^(1/7) ], Print[ n ] ], {n, 1, 10^19} ]

More terms from Sean A. Irvine, Sep 09 2022

A059005 Primes whose reversal is a tenth power.

Original entry on oeis.org

4201, 940315563074788471, 940291214439736193431, 948413222299837654933, 1081016161371207738841, 4243031147170261950811, 428799714836577410775151, 671856480838442730716731, 1049138260426397606038531, 4224428884713520708904251, 9425086013565224928896521

Offset: 1

Robert G. Wilson v, Jan 16 2001

Robert Israel, Table of n, a(n) for n = 1..9149

Cf. A007488.

rev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
S:= {}:
for i from 1 to 999 do
  if i mod 10 = 0 then next fi;
  p:= rev(i^10);
  if isprime(p) then S:= S union {p} fi;
od:
sort(convert(S, list)); # Robert Israel, Dec 22 2024

Union[Select[FromDigits[Reverse[IntegerDigits[#]]]&/@(Range[300]^10),PrimeQ]] (* Harvey P. Dale, Mar 19 2013 *)

More terms from Sean A. Irvine, Sep 09 2022

A068989 Squares which when reversed are primes (ignore leading zeros).

Original entry on oeis.org

16, 196, 361, 784, 1024, 1369, 1444, 1600, 1681, 3844, 7225, 7921, 9025, 9409, 11236, 14161, 18496, 19321, 19600, 36100, 37249, 38416, 70756, 73441, 75076, 76729, 78400, 78961, 97969, 99856, 102400, 105625, 107584, 109561, 111556, 112225

Offset: 1

Joseph L. Pe, Mar 12 2002

			40^2 = 1600. Reversing the digits we get 0061, which is the prime 61 padded with leading zeroes. Hence 1600 is in the sequence.
41^2 = 1681. Reversing the digits we get 1861, which is a prime. Hence 1681 is in the sequence.
42^2 = 1764. Reversing the digits we get 4671 = 3^3 * 173. So 1764 is not in the sequence.

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. primes whose reversal is a square, A007488; numbers n such that n^2 reversed is a prime, A059007.

Do[s = i^2; If[PrimeQ[FromDigits[Reverse[IntegerDigits[s]]]], Print[s]], {i, 1, 10^2}] (* Pe *)
Select[Range[100]^2, PrimeQ[FromDigits[Reverse[IntegerDigits[#]]]] &] (* Alonso del Arte, Jan 07 2018 *)

isok(n) = issquare(n) && isprime(fromdigits(Vecrev(digits(n)))); \\ Michel Marcus, Jan 07 2018

More terms from Zak Seidov, Jan 26 2005

Edited by N. J. A. Sloane, Dec 23 2007

A069798 Primes whose digit reversal is a nontrivial power.

Original entry on oeis.org

23, 61, 163, 487, 521, 691, 821, 1297, 1861, 4201, 4441, 4483, 5209, 5227, 9049, 9631, 12391, 14437, 16141, 16987, 61483, 63211, 65707, 65899, 67057, 69481, 92767, 94273, 96979, 106303, 108061, 123031, 123373, 125329, 127291, 129643, 142771, 146857, 148249

Offset: 1

Amarnath Murthy, Apr 09 2002

			691 is in the sequence because it is prime and its reversal, 196, is a power (greater than one) of 14.

Chai Wah Wu, Table of n, a(n) for n = 1..14573

Cf. A007488, A067194.

f[n_] := Block[{a, p = ToExpression[ StringReverse[ ToString[ Prime[n]]]]}, Log[ Apply[ Times, Transpose[ FactorInteger[p]][[1]]], p]]; Prime[ Select[ Range[10^5], IntegerQ[ f[ # ]] && f[ # ] > 1 &]]

lista(nn) = {forprime(p=2, nn, if (ispower(subst(Polrev(digits(p)), x, 10)), print1(p, ", ")););} \\ Michel Marcus, Jun 03 2016

Edited, corrected and extended by Robert G. Wilson v, Apr 15 2002

Missing terms a(4), a(24), and a(26) added by Chai Wah Wu, Jun 02 2016

A067194 Sequence of prime numbers whose reverse is a nontrivial prime power (A025475).

Original entry on oeis.org

23, 61, 163, 521, 821, 1297, 1861, 4201, 9049, 9631, 12391, 14437, 16987, 92767, 94273, 96979, 108061, 123031, 125329, 127291, 142771, 148249, 165901, 180289, 270131, 906421, 906727, 906751, 921931, 942013, 942691, 965443, 969407, 986641

Offset: 1

Shyam Sunder Gupta, Feb 19 2002

			23 is a prime and its reversal is 32 = 2^5.

Chai Wah Wu, Table of n, a(n) for n = 1..16435

Cf. A025475, A007488, A069798.

a = {}; Do[ If[ PrimeQ[n], b = ToExpression[ StringReverse[ ToString[n]]]; If[ !PrimeQ[b] && Mod[b, b - EulerPhi[b]] == 0, a = Append[a, n]]], {n, 1, 10^6} ]; a
Select[Prime[Range[80000]],PrimePowerQ[IntegerReverse[#]]&& CompositeQ[ IntegerReverse[ #]]&] (* Harvey P. Dale, Dec 25 2021 *)

lista(nn) = {forprime(p=2, nn, if (ispower(subst(Polrev(digits(p)), x, 10),,&pp) && isprime(pp), print1(p, ", ")););} \\ Michel Marcus, Jun 03 2016

Edited and extended by Robert G. Wilson v, Feb 19 2002 and Feb 24 2002

A306301 Numbers k such that k^2 reversed is a prime and k^2+(k^2 reversed) is a prime.

Original entry on oeis.org

14, 136, 190, 266, 280, 1036, 1060, 1306, 1406, 1898, 1934, 2660, 2686, 2746, 2776, 3112, 10040, 10250, 10546, 10550, 10630, 10880, 11090, 11156, 11204, 11276, 11354, 11386, 11474, 11740, 11804, 11914, 12064, 12136, 12194, 12250, 12410, 12524, 12626, 12710, 12770, 12794, 12916, 13060

Offset: 1

Robert Price, Mar 31 2019

All terms are even and not divisible by 3. - Robert Israel, Apr 09 2019

			14 is a term because 691 (the reverse of 14^2=196) and 196+691=887 are two prime numbers.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007488, A059007, A307046.

revdigs:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(k) local v; v:= revdigs(k^2); isprime(v) and isprime(v+k^2) end proc:
select(filter, [seq(seq(6*i+j,j=[2,4]),i=0..10000)]); # Robert Israel, Apr 09 2019

Select[Range[50000], PrimeQ[IntegerReverse[#^2]] && PrimeQ[#^2 + IntegerReverse[#^2]] &]

isok(k) = my(kk=fromdigits(Vecrev(digits(k^2)))); isprime(kk) && isprime(k^2+kk); \\ Michel Marcus, Apr 01 2019

A307046 Numbers k such that k^2 reversed is a prime and k^2 + (k^2 reversed) is a semiprime.

Original entry on oeis.org

4, 28, 40, 62, 106, 140, 193, 196, 274, 316, 334, 400, 410, 554, 556, 620, 862, 866, 874, 884, 962, 1004, 1025, 1066, 1154, 1174, 1190, 1205, 1256, 1274, 1294, 1360, 1390, 1394, 1396, 1400, 1744, 1784, 1816, 1844, 1891, 1900, 1927, 1960, 1981, 1988, 2672, 2696, 2710, 2722, 2740, 2786, 2800, 3016, 3026

Offset: 1

Robert Price, Mar 31 2019

			4^2=16, reversed is 61. 16+61=77 which is semiprime (7*11), so 4 is in this sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007488, A059007, A306301.

revdigs:= proc(n) local L,i;
L:= convert(n,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(n) local a,b;
a:= n^2;
b:= revdigs(a);
isprime(b) and numtheory:-bigomega(a+b)=2
end proc:
select(filter, [$1..10000]); # Robert Israel, Mar 31 2019

Select[Range[50000],
PrimeQ[IntegerReverse[#^2]] &&
   PrimeOmega[#^2 + IntegerReverse[#^2]] == 2 &]

A350363 Primes whose reversal is a ninth power.

Original entry on oeis.org

23888027348153, 17571893445665616311, 3627487775963728773631, 5213075488148035940813, 232364835105859429802371, 1648344985192619771689693, 6522990445513252220198849, 6771520922071318266744521, 23295376285906990980268061, 29758574646480445207299379

Offset: 1

Mohammed Yaseen, Dec 27 2021

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A002239, A004086, A059210.

Primes whose reversal is a k-th power: A007488 (k=2), A057699 (k=3), A058996 (k=4), A059000 (k=5), A059001 (k=6), A059002 (k=7), A059003 (k=8), A059005 (k=10).

Union[(i=IntegerReverse)@Select[Range@1000^9,PrimeQ@i@#&]] (* Giorgos Kalogeropoulos, Jan 04 2022 *)
Select[IntegerReverse/@(Range[1000]^9),PrimeQ]//Union (* Harvey P. Dale, Nov 27 2024 *)

flip(n)=fromdigits(Vecrev(digits(n))) \\ A004086
Set(select(isprime, vector(1000, n, flip(n^9)))) \\ adapted from A057699

from sympy import isprime
flip9 = (int(str(k**9)[::-1]) for k in range(1, 1000) if k%10)
print(sorted(filter(isprime, flip9))) # Michael S. Branicky, Jan 02 2022

A059004 Smallest prime whose reversal is an n-th power.

Original entry on oeis.org

2, 61, 521, 61, 23, 61277761, 821, 61277761, 23888027348153, 4201, 33670369817243, 61277761, 5265674839116110941, 441435249928911950281, 23888027348153, 1232787935486158110509626783, 270131

Offset: 1

Robert G. Wilson v, Jan 16 2001

Robert Israel, Table of n, a(n) for n = 1..271

Cf. A007488.

revdigs:= proc(n) local L,k;
  L:= convert(n,base,10);
  add(L[-k]*10^(k-1),k=1..nops(L))
end proc:
f:= proc(n) local d, k, wmin,  v,w;
  wmin:= infinity;
  for d from 1 do
    for k from ceil(10^(d/n)) do
      v:= k^n;
      if v >= 10^(d+1) then break fi;
      w:= revdigs(v);
      if isprime(w) and w < wmin then wmin:= w fi;
    od;
    if wmin < infinity then return wmin fi
  od
end proc:
map(f, [$1..20]); # Robert Israel, May 22 2019

Do[ k = 1; While[ r = ToExpression[ StringReverse[ ToString[ k^n ] ] ]; ! PrimeQ[ r ], k++ ]; Print[ r ], {n, 1, 25} ]

A167218 Primes whose reversal - 1 is a square.

Original entry on oeis.org

2, 5, 71, 73, 101, 109, 263, 269, 523, 541, 587, 1061, 1063, 2089, 2251, 2273, 2297, 2843, 2861, 5441, 5477, 5483, 6203, 6221, 7129, 7507, 7937, 10009, 10163, 10169, 10487, 10691, 20201, 20693, 22391, 22769, 24023, 24877, 26141, 26171, 26723

Offset: 1

Claudio Meller, Oct 30 2009

The first digit of a(n) cannot be 3, 4, 8 or 9. - Altug Alkan, Dec 20 2015

			71 is prime and 17-1 = 16 = 4^2.

Chai Wah Wu, Table of n, a(n) for n = 1..7256

Cf. A007488.

lista(nn) = {forprime(p=2, nn, if (issquare(eval(concat(Vecrev(Str(p))))-1), print1(p, ", ")););} \\ Michel Marcus, Dec 20 2015

from sympy import isprime
A167218_list, i, j = [], 0, 1
while j < 10**10:
    p = int(str(j)[::-1])
    if j % 10 and isprime(p):
        A167218_list.append(p)
    j += 2*i+1
    i += 1
A167218_list = sorted(A167218_list) # Chai Wah Wu, Dec 20 2015

cp's OEIS Frontend

A059002 Primes whose reversal is a seventh power.

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A059005 Primes whose reversal is a tenth power.

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A068989 Squares which when reversed are primes (ignore leading zeros).

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A069798 Primes whose digit reversal is a nontrivial power.

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A067194 Sequence of prime numbers whose reverse is a nontrivial prime power (A025475).

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A306301 Numbers k such that k^2 reversed is a prime and k^2+(k^2 reversed) is a prime.

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A307046 Numbers k such that k^2 reversed is a prime and k^2 + (k^2 reversed) is a semiprime.

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A350363 Primes whose reversal is a ninth power.

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