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A126658
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Prime numbers that are the sum of three distinct positive eighth powers.
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4
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72353, 1745153, 7444673, 44726593, 49202147, 61503553, 100006817, 100072097, 101686177, 107444417, 143046977, 214756067, 257412163, 430372577, 431661313, 435812033, 447149537, 452523713, 489805633, 530372321, 744340577, 834187553
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| These are also the sum of three squares and the sum of three fourth powers: 7444673 = 16^2 + 1296^2 + 2401^2 = 4^4 + 36^4 + 49^4 = 256 + 1679616 + 5764801.
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EXAMPLE
| 72353 = 2^8 + 3^8 + 4^8 = 256 + 6561 + 65536.
7444673 = 2^8 + 6^8 + 7^8 = 256 + 1679616 + 5764801.
49202147 = 5^8 + 7^8 + 9^8 = 390625 + 5764801 + 43046721.
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PROG
| (PARI) {m=14; p=m^8; v=vector(m, x, x^8); w=[]; for(i=1, m-2, for(j=i+1, m-1, for(k=j+1, m, if((n=v[i]+v[j]+v[k])<p&&isprime(n), w=concat(w, n))))); w=listsort(List(w), 1); for(j=1, #w-1, print1(w[j], ", "))} /* Klaus Brockhaus, Feb 11 2007 */
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CROSSREFS
| Cf. A125516, A126657.
Sequence in context: A080477 A187137 A185842 * A183788 A093212 A114258
Adjacent sequences: A126655 A126656 A126657 * A126659 A126660 A126661
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KEYWORD
| nonn
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AUTHOR
| Tomas Xordan (xordan.tom(AT)gmail.com), Feb 09 2007
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EXTENSIONS
| Edited, corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 11 2007
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