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 A270696 Perfect powers that are the average of two consecutive primes. 1
 4, 9, 64, 81, 144, 225, 324, 441, 625, 1089, 1681, 1728, 2601, 3600, 4096, 5184, 6084, 8464, 12544, 13689, 16641, 17576, 19044, 19600, 21952, 25281, 27225, 28224, 29584, 36864, 38025, 39204, 45369, 46656, 47524, 51984, 56169, 74529, 87025, 88804, 91809, 92416, 95481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding lesser primes are in A242380. - Michel Marcus, Mar 23 2016 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 1728 is a term because 1728 = 12^3 = (1723 + 1733)/2. PROG (PARI) for(n=2, 1e5, if((nextprime(n) - n) == (n - precprime(n)) && ispower(n), print1(n, ", "))); (PARI) list(lim)=my(v=List(), t); forprime(e=2, logint(lim\=1, 2), for(m=2, sqrtnint(lim, e), t=m^e; if(t-precprime(t)==nextprime(t)-t, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 21 2016 CROSSREFS Cf. A001597, A024675, A242380. Sequence in context: A062758 A217854 A028822 * A069495 A029788 A062826 Adjacent sequences:  A270693 A270694 A270695 * A270697 A270698 A270699 KEYWORD nonn AUTHOR Altug Alkan, Mar 21 2016 STATUS approved

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Last modified February 17 18:37 EST 2020. Contains 332005 sequences. (Running on oeis4.)