A132214
Numbers that are sums of seventh powers of two distinct primes.
Original entry on oeis.org
2315, 78253, 80312, 823671, 825730, 901668, 19487299, 19489358, 19565296, 20310714, 62748645, 62750704, 62826642, 63572060, 82235688, 410338801, 410340860, 410416798, 411162216, 429825844, 473087190, 893871867, 893873926
Offset: 1
a(1) = 2^7 + 3^7 = 2315 = 5 * 463.
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P:= select(isprime, [2,seq(i,i=3..100,2)]): nP:= nops(P):
N:= 2^7 + P[-1]^7:
sort(convert(select(`<=`, {seq(seq(P[i]^7+P[j]^7,j=i+1..nP),i=1..nP-1)},N),list)); # Robert Israel, Jul 01 2024
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Select[Sort[ Flatten[Table[Prime[n]^7 + Prime[k]^7, {n, 15}, {k, n - 1}]]], # <= Prime[15^7] &]
Union[Total/@(Subsets[Prime[Range[10]],{2}]^7)] (* Harvey P. Dale, Jan 03 2012 *)
A132216
Primes that are sums of eighth powers of two distinct primes.
Original entry on oeis.org
815730977, 124097929967680577, 6115597639891380737, 144086718355753024097, 524320466699664691937, 3377940044732998170977, 10094089678769799935777, 30706777728209453204417, 58310148000746221725857
Offset: 1
a(1) = 2^8 + 13^8 = 256 + 815730721 = 815730977, which is prime.
a(2) = 2^8 + 137^8 = 124097929967680577, which is prime.
a(3) = 2^8 + 223^8 = 6115597639891380737, which is prime.
a(4) = 2^8 + 331^8 = 144086718355753024097, which is prime.
a(5) = 2^8 + 389^8 = 524320466699664691937, which is prime.
a(6) = 2^8 + 491^8 = 3377940044732998170977, which is prime.
a(7) = 2^8 + 563^8 = 10094089678769799935777, which is prime.
Original entry on oeis.org
13, 107, 101, 491, 8039, 9349
Offset: 1
a(1) = 13 because 13 is the first prime p such that 2^2^3 + p^2^3 is prime.
a(2) = 107 because 107 is the 2nd prime p such that 2^2^4 + p^2^4 is prime.
a(3) = 101 because 101 is the 3rd prime p such that 2^2^5 + p^2^5 is prime.
Cf.
A000040,
A001016,
A050997,
A120398,
A122616,
A130873,
A130555,
A132214,
A132215,
A132216,
A132260.
Showing 1-3 of 3 results.
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