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A244186
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Primes which are the concatenation of five consecutive primes p, q, r, s, t while the sum (p + q + r + s + t) is another prime.
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1
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711131719, 5359616771, 6771737983, 149151157163167, 401409419421431, 479487491499503, 757761769773787, 14091423142714291433, 18111823183118471861, 21132129213121372141, 26892693269927072711, 27192729273127412749, 36133617362336313637, 37613767376937793793
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OFFSET
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1,1
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COMMENTS
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Subsequence of A086041.
Numbers: Concatenation of 5 consecutive primes at A132905.
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LINKS
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K. D. Bajpai, Table of n, a(n) for n = 1..1703
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EXAMPLE
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711131719 is in the sequence because the concatenation of [7, 11, 13, 17, 19] = 711131719 which is prime. The sum [7 + 11 + 13 + 17 + 19] = 67 is another prime.
5359616771 is in the sequence because the concatenation of [53, 59, 61, 67, 71] = 5359616771 which is prime. The sum [53 + 59 + 61 + 67 + 71] = 311 is another prime.
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MAPLE
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with(numtheory);
T:=proc(t) local w, x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
P:=proc(q) local a, b, c, d, k, i, n;
for n from 1 to q do a:=ithprime(n+4); b:=ithprime(n+3); c:=ithprime(n+2); d:=ithprime(n+1);
if isprime(a+b+c+d+ithprime(n)) then k:=a+b*10^T(a); i:=c*10^T(k); k:=k+i; i:=d*10^T(k);
k:=k+i; i:=ithprime(n)*10^T(k); k:=k+i; if isprime(k) then print(k); fi; fi;
od; end: P(10^4); # Paolo P. Lava, Jul 11 2014
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MATHEMATICA
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FromDigits[Flatten[IntegerDigits/@#]]&/@Select[Partition[Prime[Range[ 1000]], 5, 1], AllTrue[{Total[#], FromDigits[Flatten[ IntegerDigits/@ #]]}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 24 2014 *)
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CROSSREFS
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Cf. A000040, A086041, A034961, A034962, A132903, A244163.
Sequence in context: A203933 A219279 A086041 * A035518 A104952 A015370
Adjacent sequences: A244183 A244184 A244185 * A244187 A244188 A244189
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KEYWORD
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nonn,base
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AUTHOR
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K. D. Bajpai, Jun 21 2014
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STATUS
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approved
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