A339624 Perfect powers p^k, k >= 2 of palindromic primes p when p^k is not a palindrome.
16, 25, 27, 32, 49, 64, 81, 125, 128, 243, 256, 512, 625, 729, 1024, 2048, 2187, 2401, 3125, 4096, 6561, 8192, 15625, 16384, 16807, 17161, 19683, 22801, 32761, 32768, 36481, 59049, 65536, 78125, 97969, 117649, 124609, 131072, 139129, 146689, 161051, 177147, 262144
Offset: 1
Examples
5^2 = 25, 2^6 = 64, 3^4 = 81 are terms. 7^2 = 49 is a term, 7^3 = 343 is not a term, and 7^4 = 2401 is a term. 101^2 = 10201 and 11^4 = 14641 are not terms.
References
- Murray S. Klamkin, Problems in applied mathematics: selections from SIAM review, (1990), p. 520.
Links
- Gustavus J. Simmons, Palindromic Powers, J. Rec. Math., 3 (No. 2, 1970), 93-98 [Annotated scanned copy].
- Wikipedia, Palindromic number, Perfect Powers.
Crossrefs
Programs
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Mathematica
q[n_] := Module[{f = FactorInteger[n]}, Length[f] == 1 && f[[1, 2]] > 1 && PalindromeQ[f[[1, 1]]]]; Select[Range[10^5], !PalindromeQ[#] && q[#] &] (* Amiram Eldar, Dec 10 2020 *)
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PARI
ispal(n) = my(d=digits(n)); Vecrev(d)==d; isok(k) = my(p); isprimepower(k, &p) && isprime(p) && ispal(p) &&!ispal(k); \\ Michel Marcus, Dec 10 2020
Extensions
More terms from Amiram Eldar, Dec 10 2020
Comments