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A263675
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Numbers that are both averages of consecutive primes and nontrivial prime powers.
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3
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4, 9, 64, 81, 625, 1681, 4096, 822649, 1324801, 2411809, 2588881, 2778889, 3243601, 3636649, 3736489, 5527201, 6115729, 6405961, 8720209, 9006001, 12752041, 16056049, 16589329, 18088009, 21743569, 25230529, 29343889, 34586161, 37736449, 39150049
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OFFSET
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1,1
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COMMENTS
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Lesser of consecutive primes is in the sequence A084289.
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LINKS
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EXAMPLE
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625 is in this sequence because 625 = 5^4, nontrivial prime power, and 625 = (619+631)/2, with 619 and 631 consecutive primes.
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MAPLE
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N:= 10^10: # to get all terms <= N
Primes:= select(isprime, [2, seq(i, i=3..isqrt(N), 2)]):
S:= select(t -> t - prevprime(t) = nextprime(t)-t, {seq(seq(p^j, j=2..floor(log[p](N))), p=Primes)}):
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MATHEMATICA
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(* version >= 6 *)(#/2 + NextPrime[#]/2) & /@
Select[Prime[Range[5000000]], PrimePowerQ[#/2 + NextPrime[#]/2] &]
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PROG
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(PARI) {for(i=1, 10^8, if(isprimepower(i)>1&&i==(precprime(i-1)+nextprime(i+1))/2, print1(i, ", ")))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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