reviewed

approved

proposed

reviewed

editing

proposed

2, 7, 37, 127, 397, 3613, 18089, 162881, 1791787, 41211197, 370900973, 4821712733, 43395414737, 477349562419, 4296146062051, 227695741289567, 9335525392876531, 326743388750679161, 16663912826284638251, 583236948919962339073, 9915028131639359764313

Next 10 terms: 583236948919962339073, 9915028131639359764313,

Next 8 terms: 406516153397213750338933,24797485357230038770679749,

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

approved

editing

_Zak Seidov (zakseidov(AT)yahoo.com), _, May 28 2010

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

2, 7, 37, 127, 397, 3613, 18089, 162881, 1791787, 41211197, 370900973, 4821712733, 43395414737, 477349562419, 4296146062051, 227695741289567, 9335525392876531, 326743388750679161, 16663912826284638251

1,1

Next 10 terms: 583236948919962339073, 9915028131639359764313,

406516153397213750338933,24797485357230038770679749,

223177368215070348936118621,5579434205376758723402966617,

295710012884968212340357231241,23361091017912488774888221274279,

1518470916164311770367734382831699,56183423898079535503606172164775599.

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

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

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

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

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

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

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

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

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

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

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

Cf. A178468.

nonn

Zak Seidov (zakseidov(AT)yahoo.com), May 28 2010

approved