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Search: id:A103558
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| A103558 |
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Semiprimes of the form p^2 + q^2, where p and q are primes. |
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+0
2
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| 34, 58, 74, 146, 178, 194, 218, 298, 314, 365, 386, 458, 482, 533, 538, 554, 698, 818, 866, 965, 1082, 1202, 1322, 1418, 1538, 1658, 1685, 1706, 1853, 1858, 1874, 2018, 2042, 2138, 2218, 2234, 2258, 2498, 2642, 2813, 2818, 2858, 2978, 3098, 3218, 3338
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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p and q must be distinct, otherwise p^2 + q^2 = 2*p*p has three prime factors. - Klaus Brockhaus
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EXAMPLE
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34 is a term because 3^2 + 5^2 = 34 = 2*17; 58 is a term because 3^2 + 7^2 = 58 = 2*29; 74 is a term because 5^2 + 7^2 = 74 = 2*37.
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MATHEMATICA
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fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Sort[ Flatten[ Table[ Prime[p]^2 + Prime[q]^2, {p, 16}, {q, p - 1}]]], fQ[ # ] &] (from Robert G. Wilson v Mar 23 2005)
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PROGRAM
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(PARI) {m=53; v=[]; forprime(p=2, m, forprime(q=nextprime(p+1), m, if(bigomega(k=p^2+q^2)==2, v=concat(v, k)))); v=vecsort(v); stop=nextprime(m+1)^2; for(j=1, length(v), if(v[j]<stop, print1(v[j], ", ")))} (Brockhaus)
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CROSSREFS
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Cf. A001358, A006881.
Sequence in context: A051969 A067243 A055574 this_sequence A103686 A108610 A119454
Adjacent sequences: A103555 A103556 A103557 this_sequence A103559 A103560 A103561
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KEYWORD
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easy,nonn
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Mar 23 2005
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EXTENSIONS
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More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 23 2005
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