This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A089180 #15 May 26 2019 04:40:19 %S A089180 2,54,654926,6904737 %N 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). %C A089180 a(5) is greater than 105000000. %C A089180 The a(n)-th prime is the smallest start of n+2 consecutive primes in arithmetic progression. - _Jens Kruse Andersen_, Jun 14 2014 %H A089180 J. K. Andersen, <a href="http://primerecords.dk/cpap.htm#minimal">The minimal CPAP-k</a>. %H A089180 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 A089180 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 A089180 A000040[a(n)]=A006560(n+2). - _R. J. Mathar_, Aug 10 2007 %F A089180 a(n) = A000720(A006560(n+2)). - _Jens Kruse Andersen_, Jun 14 2014 %e A089180 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 A089180 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 A089180 Cf. A001223, A090403. %K A089180 more,nonn %O A089180 1,1 %A A089180 _Farideh Firoozbakht_, Dec 07 2003