OFFSET
1,1
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
EXAMPLE
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 26 2003
EXTENSIONS
More terms from Don Reble and Farideh Firoozbakht, Feb 17 2004
STATUS
approved