

A089180


a(n) is the smallest number m such that d(m) = d(m+1) = ... = d(m+n), where d(k) = prime(k+1)  prime(k) (A001223).


1




OFFSET

1,1


COMMENTS

a(5) is greater than 105000000.
The a(n)th prime is the smallest start of n+2 consecutive primes in arithmetic progression.  Jens Kruse Andersen, Jun 14 2014


LINKS

Table of n, a(n) for n=1..4.
J. K. Andersen, The minimal CPAPk.
L. J. Lander and T. R. Parkin, Consecutive primes in arithmetic progression, Math. Comp. vol. 21 no. 99 (1967) p. 489.
G. W. Polites, Prime Desert nTuplets, Amer. Math. Monthly vol. 95 no. 2 (1988) pp. 98104.


FORMULA

A000040[a(n)]=A006560(n+2).  R. J. Mathar, Aug 10 2007
a(n) = A000720(A006560(n+2)).  Jens Kruse Andersen, Jun 14 2014


EXAMPLE

a(3) = 659426 because d(659426) = d(659426+1) = d(659426+2) = d(6594286+3) or 9843019, 9843049, 9843079, 9843109, 9843139 are five consecutive primes with same difference and prime(659426) = 9843019 is the smallest prime number with this property.
Also a(4) = 6904737 because d(6904737) = d(6904737+1) = ... = d(6904737+4) or 121174811, 121174841, 121174871, 121174901, 121174931, 121174961 are six consecutive primes with same difference and prime(6904737) = 121174811 is the smallest prime number with this property.


CROSSREFS

Cf. A001223, A090403.
Sequence in context: A306266 A117681 A221603 * A280209 A034013 A157262
Adjacent sequences: A089177 A089178 A089179 * A089181 A089182 A089183


KEYWORD

more,nonn


AUTHOR

Farideh Firoozbakht, Dec 07 2003


STATUS

approved



