A000946 -id:A000946 - cp's OEIS frontend

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

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

A051320 Euclid-Mullin sequence (A000945) with initial value a(1)=53 instead of a(1)=2.

Original entry on oeis.org

53, 2, 107, 3, 7, 11, 2620003, 707431, 1993, 4409, 131, 17, 5, 858127, 79, 163, 19, 46061, 31, 17707, 157, 43, 3135504913004354085487249, 9893869, 149, 1001472037, 16979051, 387853, 61, 13, 227, 41, 206779, 443, 37, 1709

Offset: 1

Labos Elemer

Robert Price, Table of n, a(n) for n = 1..48

Cf. A000945, A000946, A005265, A005266.

a[1]=53; 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]=53; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 26 2015

A051321 Euclid-Mullin sequence (A000945) with initial value a(1)=59 instead of a(1)=2.

Original entry on oeis.org

59, 2, 7, 827, 3, 13, 4583, 5, 610478010871, 61, 292658543, 4483, 47, 11, 31, 43, 16453, 41, 3671, 1982639, 628319, 841476613, 449, 997793, 73, 983, 53, 28475917, 19, 673

Offset: 1

Labos Elemer

Robert Price, Table of n, a(n) for n = 1..48

Cf. A000945, A000946, A005265, A005266.

a[1]=59; 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]=59; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 04 2015

a(28)-a(48) from Robert Price, Jul 13 2015

A051322 Euclid-Mullin sequence (A000945) with initial value a(1)=61 instead of a(1)=2.

Original entry on oeis.org

61, 2, 3, 367, 7, 5, 1217, 17, 13, 59, 3271, 19, 11, 76938833, 337, 10711, 1021, 31, 83, 1290503, 15608141, 195648590992627, 109, 15983112328343713807564263439978033717550587578630760604057976854157331

Offset: 1

Labos Elemer

nonn

Tyler Busby, Table of n, a(n) for n = 1..42 (terms 1..33 from Robert Price)

Cf. A000945, A000946, A005265, A005266.

a[1]=61; 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]=61; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 04 2015

A051323 Euclid-Mullin sequence (A000945) with initial value a(1)=67 instead of a(1)=2.

Original entry on oeis.org

67, 2, 3, 13, 5227, 7, 5, 4637, 107, 23, 1889, 50929, 31, 1677554191669, 538282187, 59, 37, 17046661, 81088366624779421, 11, 6242880316142699576539967984792911, 73, 17, 1187, 101, 883, 3491, 47, 83, 852851, 317, 1493, 579707, 109, 1579145715181, 179, 1618489, 331

Offset: 1

Labos Elemer

nonn

Tyler Busby, Table of n, a(n) for n = 1..42

Cf. A000945, A000946, A005265, A005266.

a[1]=67; 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]=67; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 06 2015

a(21)-a(38) from Robert Price, Jul 12 2015

A051325 Euclid-Mullin sequence (A000945) with initial value a(1)=73 instead of a(1)=2.

Original entry on oeis.org

73, 2, 3, 439, 7, 5, 6729871, 103, 23, 92581, 13, 19, 2453563465139998636061911, 739, 3167, 47356379285063777, 463, 3673, 2918137, 41, 17, 2307841395358410336056217199460000033494100011180619106269258300884070797073446703818111

Offset: 1

Labos Elemer

Robert Price, Table of n, a(n) for n = 1..44

Cf. A000945, A000946, A005265, A005266.

a[1]=73; 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]=73; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 06 2015

A051326 Euclid-Mullin sequence (A000945) with initial value a(1)=79 instead of a(1)=2.

Original entry on oeis.org

79, 2, 3, 5, 2371, 7, 39334891, 19, 29397438602292811, 43, 167, 839, 5839, 30402153456526009093473029504929376787635911, 241815479790331, 41, 180922657, 5303, 2389, 13, 31, 11

Offset: 1

Labos Elemer

nonn

a(23) is a 122-digit prime.
a(5), a(7), a(9), a(14) and a(23) are all the product of the preceding terms + 1. - Robert Price, Jul 10 2015
a(32) requires factoring a composite 292 digit integer. - Robert Price, Sep 05 2021

Robert Price, Table of n, a(n) for n = 1..31 [corrected Sep 05, 2021]

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

a[1]=79; 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]=79; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 06 2015

a(n) = A020639(1 + Product_{k=1..n-1} a(k)), a(1) = 79.

cp's OEIS Frontend

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

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A051320 Euclid-Mullin sequence (A000945) with initial value a(1)=53 instead of a(1)=2.

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A051321 Euclid-Mullin sequence (A000945) with initial value a(1)=59 instead of a(1)=2.

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A051322 Euclid-Mullin sequence (A000945) with initial value a(1)=61 instead of a(1)=2.

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A051323 Euclid-Mullin sequence (A000945) with initial value a(1)=67 instead of a(1)=2.

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A051325 Euclid-Mullin sequence (A000945) with initial value a(1)=73 instead of a(1)=2.