A085325 a(n) is the least number m such that the minimal exponent for which reverse(m^n) = prime holds is n. Thus reverse(m^k) is composite for k = 1, .., n-1.
2, 4, 52, 61, 43, 49, 29, 8, 223, 53, 83, 59, 25, 568, 47, 221, 229, 1286, 427, 629, 637, 46, 109, 652, 458, 925, 1438, 86, 674, 535, 574, 314, 623, 173, 236, 676, 689, 205, 67, 419, 161, 976, 634, 818, 2104, 304, 26, 2392, 5012, 767, 238, 1769, 185, 3148, 3554
Offset: 1
Examples
For n = 10, a(10) = 53: This means that reverse(53^10) = 940315563074788471 is prime, but reverse(53^k) is composite for k=1, ..., 9. Also, reverse(m^10) for m < a(10) = 53 is not prime. However m > 53 is possible like, e.g., reverse(103^10) is prime. 10 as the least exponent belongs to several bases of which a(10) = 53 is the smallest one.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..245
Programs
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Mathematica
q[m_, n_] := AllTrue[Range[n - 1], CompositeQ[IntegerReverse[m^#]] &] && PrimeQ[IntegerReverse[m^n]]; a[n_] := Module[{m = 2}, While[! q[m, n], m++]; m]; Array[a, 30] (* Amiram Eldar, Feb 11 2025 *)
Extensions
More terms from Amiram Eldar, Feb 11 2025