A074809 -id:A074809 - cp's OEIS frontend

A104644 a(n) is the smallest prime divisor of the number obtained from concatenation of the first n primes.

2, 23, 5, 2357, 7, 23, 11, 7, 61, 3, 17, 7, 25391, 6899, 1597, 3, 17, 3, 1019, 3, 17, 211, 41378209, 3, 479, 3, 262343078386137703, 3, 107, 3, 643, 3, 7, 3, 13, 3, 107069, 7, 14733071537, 3, 61911427, 3, 13, 3, 31, 3, 11, 59, 7, 647, 31, 3, 13, 3, 31517, 43, 3, 19

Offset: 1

Labos Elemer, Mar 18 2005

			n=5, concatenation of {2,3,5,7,11} is 235711=7*151*223, smallest prime factor is a(5)=7.

Sean A. Irvine, Table of n, a(n) for n = 1..113
Dario Alejandro Alpern, Factorization using the Elliptic Curve Method.
Hisanori Mishima, Smarandache consecutive prime sequences (n = 1 to 100).

Cf. A019518, A020639, A074809.

Map[FactorInteger[FromDigits@ #][[1, 1]] &, Rest@ FoldList[Join @@ {#1, IntegerDigits[#2]} &, {}, Prime@ Range@ 29]] (* Michael De Vlieger, Jul 31 2017 *)

a(n) = vecmin(factor(eval(concat(concat([""], primes(n)))))[,1]); \\ Michel Marcus, Aug 01 2017

a(n) = A020639(A019518(n)). - Michel Marcus, Aug 01 2017

a(29) and further terms from Robert G. Wilson v, Mar 18 2005

Edited by Charles R Greathouse IV, Apr 23 2010

A103178 Number of divisors of the decimal concatenation of the first n primes.

Original entry on oeis.org

2, 2, 4, 2, 8, 8, 4, 8, 8, 8, 32, 24, 8, 16, 8, 16, 16, 16, 4, 8, 8, 16, 8, 24, 16, 64, 4, 32, 8, 128, 32, 32, 128, 128, 192, 16, 16, 64, 16, 768, 8, 48, 256, 128

Offset: 1

Parthasarathy Nambi, Mar 17 2005

			The number of divisors of 2 is 2, so the first term is 2.
The number of divisors of 23 is 2, so the second term is 2.
The number of divisors of 235 is 4, so the third term is 4.

Catcon News.
Patrick De Geest, Repeated Factorisation of Concatenated Primefactors of the Composite Numbers.

Cf. A000005, A019518, A074809.

Table[DivisorSigma[0, FromDigits[Flatten[Table[IntegerDigits[Prime[j]], {j, 1, n}], 1]]], {n, 1, 100}] (* Labos Elemer, Mar 18 2005 *)

a(n) = A000005(A019518(n)).

More terms from Labos Elemer, Mar 18 2005

Extended and edited by Charles R Greathouse IV, Apr 25 2010

A104645 Difference between the previous and the next primes to x, where x is the number obtained from concatenation of the first n primes (A019518).

Original entry on oeis.org

10, 6, 20, 24, 24, 60, 18, 48, 100, 48, 156, 74, 88, 68, 42, 126, 366, 106, 186, 136, 228, 104, 30, 246, 52, 218, 814, 58, 536, 174, 90, 924, 180, 298, 120, 330, 96, 508, 504, 60, 762, 588, 330, 138, 552, 726, 452, 634, 660, 354, 534, 1770, 52, 262, 834, 790, 250, 624

Offset: 2

Labos Elemer, Mar 18 2005

			For n=4, concatenate(2,3,5,7) gives 2357. The closest other primes are 2371 and 2351 and their difference is a(4)=20.

Cf. A019518, A074809, A104462, A104463.

Mathematica
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A019518(n)=my(k="");forprime(p=2,prime(n),k=Str(k,p));eval(k)
a(n)=my(k=A019518(n));nextprime(k+1)-precprime(k-1) \\ Charles R Greathouse IV, Apr 28 2010

a(n) = A151800(A019518(n)) - A151799(A019518(n)).

Corrected, extended, and edited by Charles R Greathouse IV, Apr 28 2010

cp's OEIS Frontend

A104644 a(n) is the smallest prime divisor of the number obtained from concatenation of the first n primes.

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A103178 Number of divisors of the decimal concatenation of the first n primes.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A104645 Difference between the previous and the next primes to x, where x is the number obtained from concatenation of the first n primes (A019518).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions