Search: a215599 -id:a215599
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A215607
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Primes p such that four consecutive primes starting with p are congruent to {1,2,3,4} (mod 5).
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+10
2
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251, 1741, 3301, 3631, 4051, 5101, 5281, 5381, 5531, 6311, 6361, 6841, 8641, 9901, 10861, 11491, 12451, 12541, 12641, 13451, 13591, 14741, 14891, 15791, 15901, 16481, 17471, 18211, 19471, 22441, 22811, 23321, 23761, 24391, 26171, 26371, 28921, 29311, 30091
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OFFSET
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1,1
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COMMENTS
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Indices of primes: 54, 271, 464, 508, 559, 682, 701, 709, 732, 821, 829, 881, 1076, 1221, 1321, 1386, 1486, ....
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LINKS
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EXAMPLE
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prime(54,55,56,57) = {251, 257, 263, 269} == {1,2,3,4} (mod 5).
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MATHEMATICA
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nn = 4000; p = Partition[Prime[Range[nn]], 4, 1]; t = Select[p, Mod[#, 5] == {1, 2, 3, 4} &]; Transpose[t][[1]] (* T. D. Noe, Aug 17 2012 *)
Select[Partition[Prime[Range[4000]], 4, 1], Mod[#, 5]=={1, 2, 3, 4}&][[;; , 1]] (* Harvey P. Dale, Feb 24 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A365309
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Primes p such that the six consecutive primes starting with p are congruent to {6, 5, 4, 3, 2, 1} (mod 7).
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+10
1
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73471, 307537, 634577, 777671, 1381141, 1886107, 1907527, 2449327, 2505187, 3078431, 3110771, 3299323, 4076477, 4088587, 4666801, 4829257, 4930043, 5069567, 5209301, 5416291, 5513941, 5711551, 6049567, 6053627, 6217091, 7216691, 8057867, 8352301, 8476817, 8635717, 8821231, 8848811, 9073819
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The six consecutive primes starting with a(3) = 634577 are 634577, 634597, 634603, 634609, 634643, 634649, which are congruent to 6, 5, 4, 3, 2, 1 respectively (mod 7).
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MAPLE
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P:= [0$6]: P7:= [0$6]: E:= [seq(i, i=6..1, -1)];
R:= NULL: count:= 0: p:= 0:
while count < 10 do
p:= nextprime(p);
P:= [op(P[2..6]), p];;
P7:= [op(P7[2..6]), p mod 7];
if P7 = E then count:= count+1; R:= R, P[1]; fi
od:
R;
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MATHEMATICA
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Prime/@SequencePosition[Mod[Prime[Range[610000]], 7], {6, 5, 4, 3, 2, 1}][[;; , 1]] (* Harvey P. Dale, Sep 20 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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