Revision History for A263015
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#23 by N. J. A. Sloane at Sat Nov 28 19:16:15 EST 2015
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#22 by Altug Alkan at Fri Nov 27 07:22:09 EST 2015
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#21 by Altug Alkan at Fri Nov 27 07:16:17 EST 2015
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| COMMENTS
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Integers n such that sum of the first n primes is the sum of 2 nonzero squares. Initial values of corresponding sum of first n primes are 2, 5, 10, 17, 41, 58, 100, 160, 197 and 281.
Initial values of corresponding sum of first n primes are 2, 5, 10, 17, 41, 58, 100, 160, 197 and 281.
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#20 by Altug Alkan at Fri Nov 27 07:12:00 EST 2015
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| NAME
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allocatedIntegers n such that A007504(n) is the sum of for2 Altugnonzero Alkansquares.
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| DATA
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1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 15, 21, 25, 29, 35, 55, 58, 59, 64, 71, 85, 89, 93, 94, 95, 100, 101, 102, 108, 112, 114, 116, 122, 124, 130, 131, 133, 135, 141, 146, 147, 151, 159, 162, 165, 170, 171, 172, 177, 178, 183, 190, 192, 193, 194, 204, 205, 206
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| OFFSET
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1,2
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| COMMENTS
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Integers n such that sum of the first n primes is the sum of 2 nonzero squares. Initial values of corresponding sum of first n primes are 2, 5, 10, 17, 41, 58, 100, 160, 197 and 281.
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| EXAMPLE
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a(3) = 3 because 2 + 3 + 5 = 3^2 + 1^2.
a(5) = 6 because 2 + 3 + 5 + 7 + 11 + 13 = 5^2 + 4^2.
a(6) = 7 because 2 + 3 + 5 + 7 + 11 + 13 + 17 = 7^2 + 3^2.
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| PROG
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(PARI) a(n) = sum(k=1, n, prime(k));
is(n) = { for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)) }
for(n=1, 1e3, if(is((a(n))), print1(n, ", ")))
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| CROSSREFS
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Cf. A000404, A007504.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Altug Alkan, Nov 27 2015
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| STATUS
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approved
editing
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#19 by Altug Alkan at Fri Nov 27 07:12:00 EST 2015
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| NAME
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allocated for Altug Alkan
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| KEYWORD
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recycled
allocated
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#18 by N. J. A. Sloane at Fri Nov 27 00:12:36 EST 2015
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#17 by N. J. A. Sloane at Fri Nov 27 00:12:32 EST 2015
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| NAME
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Numbers n such that A263014(n)=0.
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| DATA
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95
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| OFFSET
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1,2
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| COMMENTS
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Complement of A263016.
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| MATHEMATICA
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Sp[n_, k_] := Mod[Sum[If[GCD[a^2 + b^2, n] == 1, PowerMod[(a + b I), k, n], 0], {a, n}, {b, n}], n]; Select[Range[100], Sp[#, #] == 0 &]
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| CROSSREFS
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Cf. A263014, A263016.
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| KEYWORD
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nonn
recycled
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| AUTHOR
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José María Grau Ribas, Oct 07 2015
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| STATUS
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proposed
editing
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#16 by Michel Marcus at Wed Oct 14 15:18:52 EDT 2015
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Discussion
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| Fri Nov 27
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| N. J. A. Sloane: I don' think this deserves its own sequence - a sequence that starts 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 has to be pretty important to get included! Will recycle.
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#15 by Michel Marcus at Wed Oct 14 15:18:47 EDT 2015
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| COMMENTS
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complementComplement of A263016.
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| STATUS
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proposed
editing
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#14 by José María Grau Ribas at Wed Oct 14 13:31:55 EDT 2015
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