A088251 A088250(n) + 1.

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

Offset: 1

Author

Amarnath Murthy, Sep 26 2003

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A002110, A088250, A088252.

Extensions

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