A245360 Perfect powers which are the sum of two consecutive primes.
8, 36, 100, 128, 144, 216, 576, 1764, 2304, 3844, 5184, 7056, 8100, 8192, 12100, 14400, 14884, 21952, 30276, 41616, 43264, 48400, 53824, 57600, 69696, 74088, 93636, 106276, 112896, 138384, 148996, 166464, 168100, 197136, 206116, 207936, 219024, 220900, 224676, 272484, 279936
Offset: 1
Keywords
Examples
47 + 53 = 100 = 10^2, so 100 is a member of this sequence.
Links
- Jens Kruse Andersen, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Select[Total/@Partition[Prime[Range[13100]],2,1],GCD@@FactorInteger[#][[All,2]]>1&] (* Harvey P. Dale, Jan 22 2019 *)
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PARI
for(n=1,10^5,q=prime(n)+prime(n+1);if(ispower(q),print1(q,", ")))
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PARI
m=10^8; v=[]; forstep(b=2, sqrt(m), 2, forprime(p=2, 40, n=b^p; if(n>m,break); if(n==precprime(n/2)+nextprime(n/2+1), v=concat(v,n)))); v=vecsort(v) \\ Faster program. Jens Kruse Andersen, Jul 20 2014