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A088251 A088250(n) + 1. 4

%I #10 Oct 19 2017 03:14:24

%S 2,2,3,331,10831,25411,512821,512821,12960606121,434491727671,

%T 1893245380951,71023095613471,878232256181281

%N A088250(n) + 1.

%C 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.

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

%C Minimal primes p beginning a chain of n primes in an arithmetic progression of common difference p-1. - _Robin Garcia_, Jun 22 2013

%C Least prime p such that pi = i*p-i+1 is prime for i = 2 to i = n. - _Robin Garcia_, Jun 22 2013

%C 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

%e 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.

%e 2

%e 2 3

%e 3 5 7

%e 331 661 991 1321

%e ...

%e Sequence contains the first column.

%Y Cf. A002110, A088250, A088252.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Sep 26 2003

%E More terms from _Don Reble_ and _Farideh Firoozbakht_, Feb 17 2004

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)