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1, 3, 6, 11, 18, 26, 36, 48, 61, 79, 99, 126, 154, 187, 224, 266, 311, 358, 413, 471, 531, 593, 656, 721, 788, 861, 936, 1014, 1094, 1179, 1267, 1357, 1449, 1551, 1654, 1759, 1871, 1986, 2104, 2224, 2349, 2477, 2607, 2739, 2874, 3014, 3156, 3306, 3459, 3616
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refs;
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history;
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..50.
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FORMULA
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a(n) = SUM[i=1..n] A001912(i) = SUM[j=1..n] {Numbers i_j such that 4*(i_j)^2 + 1 is prime}.
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EXAMPLE
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a(17) = 1 + 2 + 3 + 5 + 7 + 8 + 10 + 12 + 13 + 18 + 20 + 27 + 28 + 33 + 37 + 42 + 45 = 311 which is itself a prime. The primes in this sequence begin: 3, 11, 61, 79, 311, 593.
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MAPLE
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A001912 := proc(n) option remember ; local a ; if n <= 3 then RETURN(n); else for a from A001912(n-1)+1 do if isprime(4*a^2+1) then RETURN(a) ; fi ; od: fi ; end: A140126 := proc(n) local i ; add( A001912(i), i=1..n) ; end: seq(A140126(n), n=1..80) ; # R. J. Mathar, Jun 12 2008
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MATHEMATICA
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Accumulate[Select[Range[200], PrimeQ[4#^2+1]&]] (* Harvey P. Dale, Jan 29 2017 *)
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CROSSREFS
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Cf. A000040, A001912, A002496, A005574, A062325, A090693.
Sequence in context: A024667 A025210 A340648 * A140235 A224214 A010000
Adjacent sequences: A140123 A140124 A140125 * A140127 A140128 A140129
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Jun 04 2008
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EXTENSIONS
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More terms from R. J. Mathar, Jun 12 2008
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STATUS
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approved
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