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A088251 A088250(n) + 1. 4
2, 2, 3, 331, 10831, 25411, 512821, 512821, 12960606121, 434491727671, 1893245380951, 71023095613471, 878232256181281 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=1..13.

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

Cf. A002110, A088250, A088252.

Sequence in context: A027498 A094877 A006560 * A229627 A140839 A320299

Adjacent sequences:  A088248 A088249 A088250 * A088252 A088253 A088254

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Sep 26 2003

EXTENSIONS

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

STATUS

approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)