A005265 -id:A005265 - cp's OEIS frontend

A240804 a(n) = -2 + product of first n odd primes.

1, 13, 103, 1153, 15013, 255253, 4849843, 111546433, 3234846613, 100280245063, 3710369067403, 152125131763603, 6541380665835013, 307444891294245703, 16294579238595022363, 961380175077106319533, 58644190679703485491633, 3929160775540133527939543, 278970415063349480483707693

Offset: 1

N. J. A. Sloane, Apr 14 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Des MacHale, Infinitely many proofs that there are infinitely many primes, Math. Gazette, 97 (No. 540, 2013), 495-498.

Cf. A000945, A000946, A005265, A005266, A240803.

[-2+&*[NthPrime(i+1): i in [1..n]]: n in [1..20]]; // Vincenzo Librandi, Apr 15 2014

Table[Product[Prime[k + 1], {k, 1, n}] - 2, {n, 1, 40}] (* Vincenzo Librandi, Apr 15 2014 *)
Rest[FoldList[Times,1,Prime[Range[2,20]]]]-2 (* Harvey P. Dale, Mar 17 2015 *)

a(n) = A070826(n+1)-2. - R. J. Mathar, May 03 2017

A051310 Euclid-Mullin sequence (A000945) with initial value a(1)=13 instead of a(1)=2.

Original entry on oeis.org

13, 2, 3, 79, 6163, 7, 1601, 11, 137, 5, 199, 151, 263, 983, 31, 83, 30187890723499, 23847817657, 37, 67, 9661, 251, 73, 1214623152057970133, 24597089626521443731307390760915220105471840174452030562332559181845834101711082531

Offset: 1

Labos Elemer

nonn

Robert Price, Table of n, a(n) for n = 1..36
A. R. Booker, S. A. Irvine, The Euclid-Mullin graph, arXiv preprint arXiv:1508.03039 [math.NT], 2015-2016.

Cf. A000945, A000946, A005265, A005266.

a[1]=13; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

spf(n)=factor(n)[1,1]
first(m)=my(v=vector(m)); v[1]=13; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v; \\ Anders Hellström, Aug 22 2015

A051311 Euclid-Mullin sequence (A000945) with initial value a(1)=17 instead of a(1)=2.

Original entry on oeis.org

17, 2, 5, 3, 7, 3571, 31, 395202571, 13, 29, 137, 23, 97, 1896893, 34138453466895150823580146142491, 4639, 61, 181, 43, 19, 11, 59, 25292522503108044617, 4909, 18305191, 467

Offset: 1

Labos Elemer

nonn

Robert Price, Table of n, a(n) for n = 1..30

Cf. A000945, A000946, A005265, A005266.

a[1]=17; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

spf(n)=factor(n)[1,1]
first(m)=my(v=vector(m)); v[1]=17; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v; \\ Anders Hellström, Aug 22 2015

A051313 Euclid-Mullin sequence (A000945) with initial value a(1)=23 instead of a(1)=2.

Original entry on oeis.org

23, 2, 47, 3, 13, 84319, 7109609443, 463, 23403050994721829453179, 7, 5, 57367, 239, 40237, 10575444619218059847586376042094152838881224222904607376771, 31333, 742759, 9444637217

Offset: 1

Labos Elemer

nonn

Robert Price, Table of n, a(n) for n = 1..37

Cf. A000945, A000946, A005265, A005266.

a[1]=23; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

spf(n)=factor(n)[1, 1]
first(m)=my(v=vector(m)); v[1]=23; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v; \\ Anders Hellström, Nov 22 2015

a(18)-a(37) from Robert Price, Jul 17 2015

A051314 Euclid-Mullin sequence (A000945) with initial value a(1)=29 instead of a(1)=2.

Original entry on oeis.org

29, 2, 59, 3, 10267, 7, 5, 3689035771, 19, 396029, 489851, 2971, 179, 13, 4441009, 419, 79, 53, 3109, 538004633, 138285071, 241, 263, 443, 11, 17, 951837583454247922680798591029699, 739, 43, 181, 131, 3257, 31, 2237

Offset: 1

Labos Elemer

nonn

Tyler Busby, Table of n, a(n) for n = 1..56 (terms 1..46 from Robert Price)

Cf. A000945, A000946, A005265, A005266.

a[1]=29; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

spf(n)=factor(n)[1, 1]
first(m)=my(v=vector(m)); v[1]=29; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v; \\ Anders Hellström, Nov 21 2015

A051315 Euclid-Mullin sequence (A000945) with initial value a(1)=31 instead of a(1)=2.

Original entry on oeis.org

31, 2, 3, 11, 23, 47059, 7, 5, 89, 19, 2287, 233, 17, 647, 1607, 12637, 103, 13, 163, 4980301, 521, 83, 16561, 540233, 443516695049428313, 109, 37, 1811, 53, 487, 548519020982014152563328120144563684918808813765009178152503015356294212417026402782591

Offset: 1

Labos Elemer

Tyler Busby, Table of n, a(n) for n = 1..37 (terms 1..36 from Robert Price)

Cf. A000945, A000946, A005265, A005266.

spf:= proc(n) local F;
  F:= select(type, map(t -> t[1], ifactors(n,easy)[2]), integer);
   if F <> [] then min(F)
   else min(numtheory:-factorset(n))
   fi
end proc:
a[1]:= 31:
for i from 2 to 31 do
  a[i]:= spf(1 + mul(a[j],j=1..i-1))
od:
seq(a[i],i=1..31); # Robert Israel, Nov 25 2015

a[1]=31; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

gpf(n)=my(f=factor(n)[, 1]); f[#f];
first(m)=my(v=vector(m)); v[1]=31; for(i=2, m, v[i]=gpf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 25 2015

A051316 Euclid-Mullin sequence (A000945) with initial value a(1)=37 instead of a(1)=2.

Original entry on oeis.org

37, 2, 3, 223, 31, 7, 127, 5, 11, 17, 157, 390191, 23339, 29, 283, 73, 19, 47, 381735266856929, 149, 83, 71, 311, 9791, 4007, 3101629, 207541, 2591, 13, 2414519329, 107, 41, 53

Offset: 1

Labos Elemer

nonn

a(34) is a 95-digit prime.

Tyler Busby, Table of n, a(n) for n = 1..42 (terms 1..39 from Robert Price)

Cf. A000945, A000946, A005265, A005266, A020639.

a[1]=37; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, n-1} ] ] ] ]; Array[a, 15]

spf(n)=my(f=factor(n)[1, 1]); f; \\ A020639
first(m)=my(v=vector(m)); v[1]=37; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 26 2015

a(n) = A020639(1 + Product_{k=1..n-1} a(k)), a(1) = 37.

A051317 Euclid-Mullin sequence (A000945) with initial value a(1)=41 instead of a(1)=2.

Original entry on oeis.org

41, 2, 83, 3, 7, 47, 71, 29, 653, 5, 173, 23, 103058819, 11, 389, 73161901, 168593357, 13, 45613, 347, 211, 53, 400947612985987, 28837, 35111, 913011302795748880783905085999338914209329333652950191830525020998365540320068611

Offset: 1

Labos Elemer

Robert Price, Table of n, a(n) for n = 1..37

Cf. A000945, A000946, A005265, A005266.

a[1]=41; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, n-1} ] ] ] ]; Array[a, 15]

spf(n)=my(f=factor(n)[1, 1]); f
first(m)=my(v=vector(m)); v[1]=41; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 26 2015

A051318 Euclid-Mullin sequence (A000945) with initial value a(1)=43 instead of a(1)=2.

Original entry on oeis.org

43, 2, 3, 7, 13, 53, 5, 6221671, 38709183810571, 139, 2801, 11, 17, 5471, 52662739, 23003, 30693651606209, 37, 1741, 1313797957, 887, 71, 7127, 109, 23, 97, 159227, 643679794963466223081509857, 103, 1079990819, 9539, 3143065813, 29, 3847, 89, 19, 577, 223

Offset: 1

Labos Elemer

nonn

			Product of first 28 terms +1 is 210102491806660945690525037461258737117339882568590700172677987135969766432980375 44232424110733238484973548134278212304532631, which is divisible by 103. Hence a(29)=103.

Tyler Busby, Table of n, a(n) for n = 1..51 (terms 1..43 from Robert Price)

Agrees with A000945 from 5th term. Cf. A000946, A005265, A005266.

a[1]=43; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, n-1} ] ] ] ]; Array[a, 15]

spf(n)=factor(n)[1, 1]
first(m)={my(v=vector(m),i,t=43);v[1]=43;for(i=2,m,v[i]=spf(t+1);t*=v[i];);v;} /* Anders Hellström, Jul 19 2015 */

a(31)-a(38) from Robert Price, Jul 19 2015

A051319 Euclid-Mullin sequence (A000945) with initial value a(1)=47 instead of a(1)=2.

Original entry on oeis.org

47, 2, 5, 3, 17, 23971, 7, 4022094091, 3673, 11, 32915297, 21513736430048030802333949693291, 43, 349, 613, 37, 6767927, 59, 71249, 19, 4455467, 997, 181, 593, 681271, 113, 13, 1205224649, 1699, 533327, 1361, 29

Offset: 1

Labos Elemer

nonn

Tyler Busby, Table of n, a(n) for n = 1..35
Andrew R. Booker and Sean A. Irvine, The Euclid-Mullin graph, arXiv preprint arXiv:1508.03039 [math.NT], 2015-2016.

Cf. A000945, A000946, A005265, A005266, A020639.

a[1]=47; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

spf(n)=factor(n)[1, 1]; \\ A020639
first(m)=my(v=vector(m)); v[1]=47; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 25 2015; corrected by Michel Marcus, Oct 10 2023

cp's OEIS Frontend

A240804 a(n) = -2 + product of first n odd primes.

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A051310 Euclid-Mullin sequence (A000945) with initial value a(1)=13 instead of a(1)=2.

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A051311 Euclid-Mullin sequence (A000945) with initial value a(1)=17 instead of a(1)=2.

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A051313 Euclid-Mullin sequence (A000945) with initial value a(1)=23 instead of a(1)=2.

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A051314 Euclid-Mullin sequence (A000945) with initial value a(1)=29 instead of a(1)=2.

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A051315 Euclid-Mullin sequence (A000945) with initial value a(1)=31 instead of a(1)=2.

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A051316 Euclid-Mullin sequence (A000945) with initial value a(1)=37 instead of a(1)=2.

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A051317 Euclid-Mullin sequence (A000945) with initial value a(1)=41 instead of a(1)=2.

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A051318 Euclid-Mullin sequence (A000945) with initial value a(1)=43 instead of a(1)=2.

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