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 A240981 Smallest perfect power b^e such that b^e+prime(n) is also a perfect power. 1
 25, 1, 4, 1, 16, 36, 8, 8, 4, 196, 1, 27, 8, 441, 81, 676, 841, 64, 1089, 125, 8, 49, 1681, 32, 128, 27, 25, 2197, 16, 8, 1, 125, 32, 2048, 2048, 361, 243, 6561, 49, 7396, 64, 8100, 25, 32, 6859, 125, 32, 289, 16, 27, 128, 4, 243, 1936, 32, 17161, 243, 729 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = 1 if and only if prime(n) is a Mersenne prime (A000668). Thus A059305 gives the values of n for which a(n) = 1. For all n, a(n) exists. Subsequence of A103953. For n > 1, a(n) <= ((prime(n)-1)/2)^2, since ((p-1)/2)^2 + p = ((p+1)/2)^2. - Jens Kruse Andersen, Aug 10 2014 LINKS Jens Kruse Andersen, Table of n, a(n) for n = 1..10000 EXAMPLE n=1: prime(n)=2, 25 = 5^2 and  25+5=27=3^3; n=2: prime(n)=3, 1 = 1^2 and  1+3=4=2^2; n=3: prime(n)=5, 4 = 2^2 and  4+5=9=3^2. PROG (PARI) {forprime(p=2, 200, if(ispower(1+p), print1(1", "), n=4; while(!(ispower(n)&&ispower(n+p)), n++); print1(n", ")))} CROSSREFS Cf. A000668, A001597, A103953. Sequence in context: A027431 A040638 A040641 * A040640 A098472 A040642 Adjacent sequences:  A240978 A240979 A240980 * A240982 A240983 A240984 KEYWORD nonn AUTHOR Zak Seidov, Aug 06 2014 STATUS approved

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Last modified October 21 19:17 EDT 2019. Contains 328308 sequences. (Running on oeis4.)