A088252 -id:A088252 - cp's OEIS frontend

A088250 a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.

1, 1, 2, 330, 10830, 25410, 512820, 512820, 12960606120, 434491727670, 1893245380950, 71023095613470, 878232256181280, 11429352906540438870

Offset: 1

Amarnath Murthy, Sep 26 2003

Conjectures: (1) Sequence is infinite. (2) For every n there are infinitely many arithmetic progressions with n successive primes.

Both conjectures follow from Dickson's conjecture. [Charles R Greathouse IV, Mar 14 2011]

			a(11) = 1893245380950 because all eleven numbers 1*1893245380950 + 1, 2*1893245380950 + 1, 3*1893245380950 + 1, ..., 10*1893245380950 + 1 & 11*1893245380950 + 1 are prime and 1893245380950 is the smallest number with such property.

Carlos Rivera, Puzzle 379. SG primes and its prime average, The Prime Puzzles and Problems Connection.

Cf. A088251, A088252, A088651, A125838, A125839.

a[n_] := Block[{k = If[n < 4, 1, 6], s}, s = k; While[! AllTrue[k Range[n] + 1, PrimeQ], k += s]; k]; Array[a, 8] (* Giovanni Resta, Mar 31 2017 *)

Edited by Don Reble, Sep 29 2003
Entry revised by N. J. A. Sloane, Jan 05 2007
a(14) from Giovanni Resta, Mar 31 2017

A088251 A088250(n) + 1.

Original entry on oeis.org

2, 2, 3, 331, 10831, 25411, 512821, 512821, 12960606121, 434491727671, 1893245380951, 71023095613471, 878232256181281

Offset: 1

Amarnath Murthy, Sep 26 2003

nonn

The n-th row of the following triangle contains smallest set of n primes which form n successive terms of an arithmetic progression from the 2nd to (n+1)th term with the first term 1. 2 2 3 3 5 7 331 661 991 1321 ... Sequence contains the first column.
Conjecture: (1) Sequence is infinite. (2) For every n there are infinitely many arithmetic progressions with n successive primes.
Minimal primes p beginning a chain of n primes in an arithmetic progression of common difference  p-1. - Robin Garcia, Jun 22 2013
Least prime p such that pi = i*p-i+1 is prime for i = 2 to i = n. - Robin Garcia, Jun 22 2013
a(n) is 1 mod 10 for n > 3 because if p is 3 mod 10, then all (2+5*t)*p -(1+5*t) for t=0,1,2,... are 5 mod 10; if p is 7 mod 10, all (4+5*t)*p -(3+5*t) are 5 mod 10 for t=0,1,2...;  if p is 9 mod 10, all (3+5*t)*p - (2+5*t) are 5 mod 10 for t=0,1,2... - Robin Garcia, Jun 22 2013

			The n-th row of the following triangle contains smallest set of n primes which form n successive terms of an arithmetic progression from the 2nd to (n+1)-st term with the first term 1.
2
2 3
3 5 7
331 661 991 1321
...
Sequence contains the first column.

Cf. A002110, A088250, A088252.

More terms from Don Reble and Farideh Firoozbakht, Feb 17 2004

A164325 a(n) is the smallest number m such that (2k-1)m+1 is prime for all 0

Original entry on oeis.org

1, 2, 2, 6, 1170, 64590, 25153800, 25153800, 4747505070, 207187349040, 6703860240000, 26997529639080, 1760354281625940, 1760354281625940, 10718654377787155800

Offset: 1

Farideh Firoozbakht, Sep 15 2009

Cf. A088250, A071576, A164326, A088251, A088651, A125838, A125839, A088252.

a(5) corrected by Zak Seidov, Sep 16 2009
a(10) and a(11) from Zak Seidov, Sep 17 2009
a(12)=26997529639080 from Zak Seidov, Sep 25 2009
a(13)-a(15) from Giovanni Resta, Apr 01 2017

cp's OEIS Frontend

A088250 a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A088251 A088250(n) + 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A164325 a(n) is the smallest number m such that (2k-1)m+1 is prime for all 0

Views

Author

Keywords

Crossrefs

Extensions