A000945 -id:A000945 - cp's OEIS frontend

A051312 Euclid-Mullin sequence (A000945) with initial value a(1)=19 instead of a(1)=2.

19, 2, 3, 5, 571, 271, 457, 397, 1123, 23, 103, 42572757267735264511, 313, 17, 16013177, 7951, 1259, 41, 1531, 11, 83, 53, 67, 7, 21397, 13, 1619, 1274209367143, 433, 37, 491, 29, 658837, 135202080527, 163, 587, 31, 2797, 35286479

Offset: 1

Labos Elemer

nonn

Tyler Busby, Table of n, a(n) for n = 1..50 (terms 1..42 from Robert Price)

Cf. A000945, A000946, A005265, A005266.

a[1]=19; 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]=19; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v; \\ Anders Hellström, Aug 31 2015

A051324 Euclid-Mullin sequence (A000945) with initial value a(1)=71 instead of a(1)=2.

Original entry on oeis.org

71, 2, 11, 3, 43, 201499, 67, 5, 487, 19, 967, 13, 131, 17, 3523392679146994953040171, 7, 633046028131441, 197, 1313225762816449, 22441, 29, 7039, 2357, 12264112894355231632110401532068053014661

Offset: 1

Labos Elemer

nonn

Tyler Busby, Table of n, a(n) for n = 1..44 (terms 1..29 from Robert Price)

Cf. A000945, A000946, A005265, A005266.

a[1]=71; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

spf(n)=my(f=factor(n)[1, 1]); f
first(m)=my(v=vector(m)); v[1]=71; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 04 2015

a(24) from Robert Price, Jul 11 2015

A051330 Euclid-Mullin sequence (A000945) with initial value a(1)=97 instead of a(1)=2.

Original entry on oeis.org

97, 2, 3, 11, 19, 7, 461, 719, 5, 1411130344471, 139, 43, 36599, 1097, 17, 104370954301, 23, 13, 59, 41, 83, 196777201807603861, 569, 31, 149, 131, 7408846366410141253195388029, 29, 27017, 192228034594584553, 307, 2677, 73, 263, 389, 10463, 61, 47, 617, 743

Offset: 1

Labos Elemer

Tyler Busby, Table of n, a(n) for n = 1..51 (terms 1..45 from Robert Price)
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.

a[1]=97; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]

lpf(n)=factor(n)[1, 1]
first(m)=my(v=vector(m)); v[1]=97; for(i=2, m, v[i]=lpf(1+prod(j=1, i-1, v[j]))); v; \\ Anders Hellström, Aug 31 2015

a(34)-a(45) from Robert Price, Jul 20 2015

A093779 a(n) is the position of prime 3 in the Euclid-Mullin (EM) sequence of type A000945, if it were started with prime(n) instead of 2.

Original entry on oeis.org

2, 1, 4, 3, 4, 3, 4, 3, 4, 4, 3, 3, 4, 3, 4, 4, 5, 3, 3, 4, 3, 3, 4, 4, 3, 5, 3, 4, 3, 4, 3, 4, 4, 3, 5, 3, 3, 3, 4, 4, 4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 4, 3, 4, 4, 4, 5, 3, 3, 4, 3, 4, 3, 5, 3, 4, 3, 3, 4, 3, 5, 4, 3, 3, 3, 5, 5, 3, 4, 3, 4, 3, 4, 3, 3, 4, 4, 3, 5, 3, 4, 6, 3, 4, 3, 5, 4, 5, 3, 3, 3, 4, 5, 4, 3

Offset: 1

Labos Elemer, May 03 2004

nonn

			p=3 arises first as n-th term for n=1,2,3,4 as follows: {3,2,7,43,13,53,5}, {2,3,7,43,13,53,5}, {7,2,3,43,13,53,5}, {5,2,11,3,331,19}, ... i.e., started at suitable initial primes;
p=2 arises always as 2nd or once as first term in case of various EM-sequences.

Cf. A000945, A051308-A051334, A056756, A093777, A093778.

A093780 a(n) is the smallest prime used as initial value for Euclid-Mullin (EM) sequence (of variant A000945), such that in the corresponding EM-sequence the p=3 prime arises at the n-th position.

Original entry on oeis.org

3, 2, 7, 5, 59, 479, 821, 1871, 17393, 43019, 284783, 1572149, 2737793, 32938853, 24254639

Offset: 1

Labos Elemer, May 03 2004

			p=3 arises first as n-th term for n=1,2,3,4,...,9th as follows:
{3,2,7,43,13,53,5},{2,3,7,43,13,53,5},{7,2,3,43,13,53,5},
{5,2,11,3,331,19},{269,2,7,3767,3,42559567},{479,2,7,19,5,3},
{821,2,31,109,7,509,3},{1871,2,19,7,37,13,23,3},
{17393,2,43,37,7,4129,13,5,3},

Cf. A000945, A051308-A051334, A056756, A093777-A093779.

More terms from David Wasserman, Apr 12 2007

A093781 a(n) is the position of the prime 5 in the Euclid-Mullin (EM) sequence of type A000945, if it were started with prime(n) instead of 2.

Original entry on oeis.org

7, 7, 1, 7, 18, 10, 3, 4, 11, 7, 8, 8, 10, 7, 3, 13, 8, 6, 7, 8, 6, 4, 7, 8, 9, 4, 6, 3, 4, 11, 5, 8, 3, 4, 4, 8, 8, 13, 3, 10, 21, 15, 6, 8, 3, 4, 13, 5, 3, 4, 8, 14, 6, 10, 3, 6, 12, 6, 10, 6, 6, 13, 8, 4, 6, 3, 11, 5, 3, 4, 13, 6, 10, 8, 4, 26, 8, 7, 11, 4, 7, 10, 7, 5, 4, 7, 16, 8, 7, 9, 3, 5, 5, 6

Offset: 1

Labos Elemer, May 04 2004

nonn

a(38) = 13 because prime(38) = 163 and the corresponding EM sequence is {163, 2, 3, 11, 7, 75307, 3931, 5399, 3041, 409, 179, 92958641873, 5, 2003, ...}, where 5 appears at the 13th position. - David Wasserman, Apr 19 2007

David Wasserman, Apr 19 2007, Table of n, a(n) for n = 1..1000

Cf. A000945, A051308-A051334, A056756, A093777-A093780.

Cf. A093782.

em(i) = local(p, c, n, f, q); p = prime(i); if (p == 5, return(1)); c = 1; n = p; while (1, c++; f = factor(n + 1, 2^31 - 1); q = f[1, 1]; if (!isprime(q), f = factor(n + 1); q = f[1, 1]); if (q == 5, return(c)); n *= q); \\ David Wasserman, Apr 19 2007

More terms from David Wasserman, Apr 19 2007

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

cp's OEIS Frontend

A051312 Euclid-Mullin sequence (A000945) with initial value a(1)=19 instead of a(1)=2.

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A051324 Euclid-Mullin sequence (A000945) with initial value a(1)=71 instead of a(1)=2.

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A051330 Euclid-Mullin sequence (A000945) with initial value a(1)=97 instead of a(1)=2.

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A093779 a(n) is the position of prime 3 in the Euclid-Mullin (EM) sequence of type A000945, if it were started with prime(n) instead of 2.

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A093780 a(n) is the smallest prime used as initial value for Euclid-Mullin (EM) sequence (of variant A000945), such that in the corresponding EM-sequence the p=3 prime arises at the n-th position.

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A093781 a(n) is the position of the prime 5 in the Euclid-Mullin (EM) sequence of type A000945, if it were started with prime(n) instead of 2.

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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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