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%I #15 May 26 2019 04:40:19
%S 2,54,654926,6904737
%N 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).
%C a(5) is greater than 105000000.
%C The a(n)-th prime is the smallest start of n+2 consecutive primes in arithmetic progression. - _Jens Kruse Andersen_, Jun 14 2014
%H J. K. Andersen, <a href="http://primerecords.dk/cpap.htm#minimal">The minimal CPAP-k</a>.
%H L. J. Lander and T. R. Parkin, <a href="http://dx.doi.org/10.1090/S0025-5718-1967-0222008-0">Consecutive primes in arithmetic progression</a>, Math. Comp. vol. 21 no. 99 (1967) p. 489.
%H G. W. Polites, <a href="http://www.jstor.org/stable/2323061">Prime Desert n-Tuplets</a>, Amer. Math. Monthly vol. 95 no. 2 (1988) pp. 98-104.
%F A000040[a(n)]=A006560(n+2). - _R. J. Mathar_, Aug 10 2007
%F a(n) = A000720(A006560(n+2)). - _Jens Kruse Andersen_, Jun 14 2014
%e 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.
%e 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.
%Y Cf. A001223, A090403.
%K more,nonn
%O 1,1
%A _Farideh Firoozbakht_, Dec 07 2003
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