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

1,1

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

47 + 53 = 100 = 10^2, so 100 is a member of this sequence.

Mathematica

Select[Total/@Partition[Prime[Range[13100]], 2, 1], GCD@@FactorInteger[#][[All, 2]]>1&] (* Harvey P. Dale, Jan 22 2019 *)

Prog

(PARI) for(n=1, 10^5, q=prime(n)+prime(n+1); if(ispower(q), print1(q, ", ")))
(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

Crossrefs

Cf. A091624, A062703, A226524.

Sequence in context: A224159 A321251 A035006 * A032768 A224410 A006636

Adjacent sequences: A245357 A245358 A245359 * A245361 A245362 A245363

Keyword

nonn

Author

Derek Orr, Jul 18 2014

Status

approved