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a(n) = smallest prime > a(n-1) such that (a(n-1)+a(n)) is a multiple of nextprime(a(n-1)).
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%I #6 Oct 13 2024 07:05:34

%S 2,7,37,127,397,3613,18089,162881,1791787,41211197,370900973,

%T 4821712733,43395414737,477349562419,4296146062051,227695741289567,

%U 9335525392876531,326743388750679161,16663912826284638251,583236948919962339073,9915028131639359764313

%N a(n) = smallest prime > a(n-1) such that (a(n-1)+a(n)) is a multiple of nextprime(a(n-1)).

%C Next 8 terms: 406516153397213750338933,24797485357230038770679749,

%C 223177368215070348936118621,5579434205376758723402966617,

%C 295710012884968212340357231241,23361091017912488774888221274279,

%C 1518470916164311770367734382831699,56183423898079535503606172164775599.

%e a(1)=2; a(2)=7 because 2+7=9 is a multiple of 3=nextprime(2)

%e a(3)=37 because 7+37=44 is a multiple of 11=nextprime(7)

%e 37+127=164=4*41 (41=nextprime(37))

%e 127+397=524=4*131 (131=nextprime(127))

%e 397+3613=4010=10*401 (401=nextprime(397))

%e 3613+18089=21702=6*3617 (3617=nextprime(3613))

%e 18089+162881=180970=10*18097 (18097=nextprime(18089))

%e 162881+1791787=1954668=12*162889 (162889=nextprime(162881))

%e 1791787+41211197=43002984=24*1791791 (1791791=nextprime(1791787)).

%t <<NumberTheory`NumberTheoryFunctions`; a=2;np=NextPrime[a];s={a};

%t Do[Do[If[PrimeQ[p=np*k-a],AppendTo[s,p];a=p;np=NextPrime[a];Break[]],{k,1000}],{30}];s

%Y Cf. A178468.

%K nonn

%O 1,1

%A _Zak Seidov_, May 28 2010