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).

2, 54, 654926, 6904737

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 CPAP-k.

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 n-Tuplets, Amer. Math. Monthly vol. 95 no. 2 (1988) pp. 98-104.

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: A117681 A221603 A359183 * A034013 A340211 A356985

Adjacent sequences: A089177 A089178 A089179 * A089181 A089182 A089183

Keyword

more,nonn

Author

Farideh Firoozbakht, Dec 07 2003

Status

approved