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A154736
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Define k(0) = 2 and k(m) = m^2-k(m-1) for m >= 1. This is a list of those m for which k(m)+1 and k(m)-1 are both prime.
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2
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3, 4, 16, 40, 64, 88, 208, 280, 352, 376, 460, 484, 508, 520, 604, 1012, 1024, 1072, 1168, 1240, 1264, 1336, 1420, 1432, 1444, 1912, 2176, 2212, 2548, 2560, 2632, 2836, 2848, 2872, 2944, 2956, 3184, 3220, 3508, 3616, 3640, 3772, 3868, 3892, 3928, 3940, 3952
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OFFSET
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1,1
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 1..10000
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FORMULA
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A154734(n+1) = k(a(n)) where k(m) = m*(m+1)/2+2*(-1)^m. - R. J. Mathar, Jul 16 2022
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EXAMPLE
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The initial values of k(m) are:
k(0) = 2
k(1) = 1-2 = -1
k(2) = 4+1 = 5
k(3) = 9-5 = 4 and both 3 and 5 are primes, so 3 is the first term in the sequence
k(4) = 16-4 = 12, and 11 & 13 are primes, so a(2) = 4
and so on - N. J. A. Sloane, Jul 14 2022
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MATHEMATICA
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k=2; lst={}; Do[k=n^2-k; If[PrimeQ[k-1]&&PrimeQ[k+1], AppendTo[lst, n]], {n, 8!}]; lst
(* Second program: *)
k = 2; Reap[Do[Set[k, m^2 - k]; If[AllTrue[k + {-1, 1}, PrimeQ], Sow[m]], {m, 4000}]][[-1, -1]] (* Michael De Vlieger, Jul 14 2022 *)
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PROG
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(PARI) a154736(upto, k0=2) = {my(k=k0); for(n=1, upto, my(kk=n^2-k); if(isprime(kk-1) && isprime(kk+1), print1(n, ", ")); k=kk)};
a154736(5000) \\ Hugo Pfoertner, Jul 14 2022
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CROSSREFS
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Cf. A154734.
Sequence in context: A328773 A330693 A329541 * A188114 A188116 A300316
Adjacent sequences: A154733 A154734 A154735 * A154737 A154738 A154739
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KEYWORD
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nonn
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AUTHOR
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Vladimir Joseph Stephan Orlovsky, Jan 14 2009
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EXTENSIONS
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Better name from Pontus von Brömssen, Jul 14 2022
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STATUS
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approved
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