A058998 Least exponent k for which n^k reversed (leading zeros are not allowed) is a prime, or 0 if impossible.

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

Offset

1,4

Comments

There are two different versions of this sequence: A085324 and this sequence which agrees with A085324 on the first 19 terms, but differs at a(20).

Links

Robert Israel, Table of n, a(n) for n = 1..168

Formula

a(n*10^k) = 0 for all k > 0 since definition does not allow leading 0's.

Example

a(4) is 2, because 4^2 is 16, and 16 reversed is 61 which is prime.

Maple

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 or (n/10)::integer then return 0 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..168]); # Robert Israel, Apr 08 2018

Mathematica

Do[ If[ Mod[ n, 3 ] != 0 && Mod[ n, 10 ] != 0 && Mod[ n, 11 ] != 0, k = 1; While[ !PrimeQ[ ToExpression[ StringReverse[ ToString[ n^k ] ] ] ], k++ ]; Print[ k ], Print[ 0 ] ], {n, 2, 75} ]

Crossrefs

Cf. A085324.

Sequence in context: A076422 A295861 A337272 * A085324 A264945 A326476

Adjacent sequences: A058995 A058996 A058997 * A058999 A059000 A059001

Keyword

base,nonn

Author

Robert G. Wilson v, Jan 17 2001

Status

approved