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A181619
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Numbers k such that k^2+1 = 2p,(k+1)^2+1 = 5q, (k+2)^2+1 = 10r where p, q, and r are primes.
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1
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11, 51, 61, 101, 221, 261, 571, 2271, 2821, 2871, 5071, 5651, 5761, 6561, 6951, 9751, 10461, 10851, 11621, 11711, 14961, 15911, 16551, 17171, 17601, 18511, 19071, 19551, 23151, 25261, 27351, 27751
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OFFSET
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1,1
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COMMENTS
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a(n) == 1 (mod 10).
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
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EXAMPLE
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a(2) = 51 because 51^2+1 = 2*1301, 52^2+1 = 5*541, 53^2+1 = 10*281.
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MAPLE
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with(numtheory):for n from 1 to 30000 do : x:=n^2+1:y:=(n+1)^2+1:z:=(n+2)^2+1:x1:=factorset(x):y1:=factorset(y):z1:=factorset(z):n1:=bigomega(x):n2:=bigomega(y):n3:=bigomega(z):if
x1[1]=2 and n1=2 and y1[1]=5 and n2 = 2 and z1[1]=2 and z1[2]=5 and n3=3 then
printf(`%d, `, n):else fi:od:
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MATHEMATICA
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ksQ[k_]:=And@@PrimeQ[{(k^2+1)/2, ((k+1)^2+1)/5, ((k+2)^2+1)/10}]; Select[ Range[30000], ksQ] (* Harvey P. Dale, Sep 01 2013 *)
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PROG
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(PARI) forstep(k=1, 1e5, 10, if(isprime(k^2\2+1)&isprime((k+1)^2\5+1)&isprime((k+2)^2\10+1), print1(k", ")))
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CROSSREFS
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Cf. A002144, A005574, A002731.
Sequence in context: A026618 A266034 A026684 * A067983 A175360 A226451
Adjacent sequences: A181616 A181617 A181618 * A181620 A181621 A181622
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KEYWORD
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nonn
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AUTHOR
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Michel Lagneau, Jan 31 2011
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STATUS
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approved
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