A031442
a(0) = 13; for n > 0, a(n) is the greatest prime factor of PreviousPrime(a(n-1))*a(n-1)-1 where PreviousPrime(prime(k))=prime(k-1).
Original entry on oeis.org
13, 71, 41, 379, 23561, 5431, 20269, 89, 1231, 44497, 329952671, 36583, 1126159, 90209117, 14095897, 15272393, 13887359, 256460794943, 2740505805180429880723, 1591234463080874838018721796071210709
Offset: 0
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NestList[FactorInteger[#*NextPrime[#,-1]-1][[-1,1]]&,13,20] (* Harvey P. Dale, May 26 2025 *)
More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 23 2000. a(19) and a(20) pass the strong pseudoprime test for many bases.
A082021
a(0) = 7; for n > 0, a(n) is the greatest prime factor of PP(PP(a(n-1)))*a(n-1)+2 where PP(n) is an abbreviation for PreviousPrime(n).
Original entry on oeis.org
7, 23, 131, 47, 643, 2459, 2000807, 503347241, 82125909539251, 9617692012399, 55555555342491359799151, 1116817987709786226917069, 578610396154837, 66992050984853, 254497141, 1660738053545999, 201525986561, 25600818891233, 796725607788661087, 23547857117470471
Offset: 0
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NestWhileList[FactorInteger[2+#*Prime[PrimePi[ # ]-2]][[ -1,1]] &, 7, True, 8] (* T. D. Noe, Nov 15 2006 *)
NestList[FactorInteger[NextPrime[NextPrime[#,-1],-1]#+2][[-1,1]]&,7,20] (* Harvey P. Dale, Dec 26 2017 *)
A034970
a(n) is the greatest prime factor of a(n-2)*a(n-1)-1.
Original entry on oeis.org
2, 3, 5, 7, 17, 59, 167, 821, 2539, 1042259, 508903, 5765312303, 1461701, 1404527126434567, 2034580216153, 97552206663238517, 3105563257, 46137561830961960349, 9777395920402541, 6719860896292085951563127, 5367788603966004659, 33011914147
Offset: 0
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a034970 n = a034970_list !! n
a034970_list = 2 : 3 : (map (a006530 . (subtract 1)) $
zipWith (*) a034970_list $ tail a034970_list)
-- Reinhard Zumkeller, Feb 23 2012
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with(numtheory):
a:= proc(n) option remember; `if`(n<2, n+2,
max(factorset(a(n-2)*a(n-1)-1)[]))
end:
seq(a(n), n=0..22); # Alois P. Heinz, Feb 03 2014
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a[0] = 2; a[1] = 3; a[n_] := a[n] = FactorInteger[ a[n-2]*a[n-1] - 1][[-1, 1]]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Mar 09 2012 *)
nxt[{a_,b_}]:={b,FactorInteger[a*b-1][[-1,1]]}; Transpose[NestList[nxt,{2,3},25]][[1]] (* Harvey P. Dale, Apr 05 2014 *)
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A034970(a,b) = {local(f);f=factor(a*b-1);f[matsize(f)[1],1]}
a=2;b=3;print(a);print(b)
for(n=2,28,c=A034970(a,b);print(c);a=b;b=c)
A082132
a(0) = 5; for n > 0, a(n) is the greatest prime factor of PP(a(n-1))*a(n-1)-2 where PP(n) is an abbreviation for PreviousPrime(n).
Original entry on oeis.org
5, 13, 47, 673, 1093, 4789, 15887, 6961, 7079, 1853387, 5636791, 16319158451, 46975091221, 97536826417, 9513432505744326182381, 2335222008886384800739, 7440517660385876970522347503153, 83914607657246408236765553419, 1960358081272210906656999086971746456168551
Offset: 0
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p=5;for(k=1,20,print1(p,",");p=precprime(p-1)*p-2;f=factor(p);s=matsize(f)[1];p=f[s,1]) \\ Rick L. Shepherd, Dec 19 2004
Showing 1-4 of 4 results.
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