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

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

Author

Labos Elemer

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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 */

Extensions

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