A085298 -id:A085298 - cp's OEIS frontend

A085299 a(n) is the smallest number x such that A085298[x]=n, or 0 if no such number exists.

1, 8, 47, 18, 14, 89, 10, 9, 48, 16, 23, 17, 168, 268, 15, 661, 50, 380, 84, 116, 360, 245, 29, 144, 345, 227, 785, 261, 148, 235, 691, 658, 638, 40, 1023, 674, 1529, 210, 19, 81, 181, 428, 170, 1130, 2322, 406, 600, 373, 958, 217

Offset: 1

Labos Elemer, Jun 24 2003

			a(13) = 168 means that 13 is the smallest exponent such that reversed[p(168)^13] = reversed[997^13] = 776831144302925059735912605306533496169
is prime if read in this direction and 13th prime-power if read backwards.

Cf. A085298, A057708, A058993, A056994, A059695, A003459, A007500, A055387, A061461, A068652.

A085324 a(n) is the least exponent so that reverse(n^a(n)) is a prime number. a(n)=0 if no such exponent exists, namely when e.g., n = 3k or n = 11k, k > 1.

Original entry on oeis.org

0, 1, 1, 2, 1, 0, 1, 8, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 2, 1, 0, 0, 8, 0, 13, 47, 0, 2, 7, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 2, 2, 0, 5, 0, 0, 22, 15, 0, 6, 1, 0, 3, 10, 0, 0, 143, 0, 88, 12, 0, 4, 2, 0, 4, 8, 0, 39, 83, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 8, 0, 6, 11, 0, 2, 28, 0, 0, 2, 0, 1, 1, 0, 292, 1, 0, 1, 1

Offset: 1

Labos Elemer, Jul 02 2003

a(k) = 1 for k in A095179. - Michel Marcus, Apr 09 2018

			For n=46, a(46)=22 means that reversion of 46^22 gives a prime: 6100744433653913942689966672393877083.

Robert Israel, Table of n, a(n) for n = 1..202

Cf. A085325, A085298, A085299, A085300.

Rev:= proc(n) local L;
L:= convert(n,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
f:= proc(n) local k;
  if igcd(n,33) <> 1  then return 0 fi;
  if n mod 10 = 0 then return procname(n/10) fi;
  for k from 1 do if isprime(Rev(n^k)) then return k fi od:
end proc:
f(1):= 0: f(3):= 1; f(11):= 1;
map(f, [$1..100]); # Robert Israel, Apr 09 2018

nd[x_, y_] := 10*x+y; tn[x_] := Fold[nd, 0, x]; bac[x_] := tn[Reverse[IntegerDigits[x]]] t={list without 3k and 11k numbers}; le=Length[t]; Table[f=1; Do[s=bac[Part[t, n]^k]; If[PrimeQ[s]&&Equal[f, 1], Print[{k, Part[t, n], s}]; f=0], {k, 1, 300}], {n, 1, le}]

a(3k) = a(11k) = 0 for k > 1 because reversion does not make a prime from any of their powers.

A085300 a(n) is the least prime x such that when reversed it is a power of prime(n).

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 71, 163, 18258901387, 90367894271, 13, 73, 1861, 344800741, 34351783286302805384336021, 940315563074788471, 1886172359328147919771, 14854831

Offset: 1

Labos Elemer, Jun 24 2003

A006567 (after rearranging terms) and A002385 are subsequences. - Chai Wah Wu, Jun 02 2016

			a(14)=344800741 means that 147008443=43^5=p(14)^5, where 5 is the smallest such exponent;
a(19) has 82 decimal digits and if reversed equals 39th power of p(19)=67.

Chai Wah Wu, Table of n, a(n) for n = 1..86

Cf. A085298, A057708, A058993, A056994, A059695, A003459, A007500, A055387, A061461, A068652.

from sympy import prime, isprime
def A085300(n):
    p = prime(n)
    q = p
    while True:
        m = int(str(q)[::-1])
        if isprime(m):
            return(m)
        q *= p # Chai Wah Wu, Jun 02 2016

A085326 a(n)=p is smallest prime such that rev(p)=n^j with some exponent, or 0 if no such prime exists [when e.g. n=1,n=3k or n=11k, k>1].

Original entry on oeis.org

0, 2, 3, 61, 5, 0, 7, 61277761, 0, 0, 11, 0, 31, 41, 0, 61, 71, 0, 163, 2, 0, 0, 18258901387, 0, 5265674839116110941, 6716872795737314976899264656807717363719079328404119318887571869813, 0

Offset: 1

Labos Elemer, Jul 03 2003

			n=86: a(86)=6505868216024313214870917495263873755562243530151045641,
and rev[86]=86^28.

Cf. A085298, A085299, A085300, A085324, A085325.

cp's OEIS Frontend

A085299 a(n) is the smallest number x such that A085298[x]=n, or 0 if no such number exists.

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A085324 a(n) is the least exponent so that reverse(n^a(n)) is a prime number. a(n)=0 if no such exponent exists, namely when e.g., n = 3k or n = 11k, k > 1.

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A085300 a(n) is the least prime x such that when reversed it is a power of prime(n).

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A085326 a(n)=p is smallest prime such that rev(p)=n^j with some exponent, or 0 if no such prime exists [when e.g. n=1,n=3k or n=11k, k>1].

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