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A257762 Numbers n with property that A062234(n) = A062234(n+1).

%I A257762 #29 Sep 08 2022 08:46:12
%S A257762 1,3,5,7,13,26,28,43,49,64,69,78,89,93,96,116,131,134,142,148,152,155,
%T A257762 167,182,202,206,212,225,231,234,236,238,247,253,258,281,286,302,303,
%U A257762 311,313,330,332,333,334,336,337,356,362,384,385,390,435,438,455,458,484,492,512,516
%N A257762 Numbers n with property that A062234(n) = A062234(n+1).
%C A257762 Numbers n with property that 2*prime(n)-prime(n+1) = 2*prime(n+1)-prime(n+2), or 2*prime(n)+prime(n+2) = 3*prime(n+1).
%C A257762 Numbers n with property that 2*A001223(n) = A001223(n+1). - _Gionata Neri_, May 22 2015
%C A257762 a(n) = A258432(m), where m such that A258383(m) = 2. - _Reinhard Zumkeller_, May 31 2015
%H A257762 Robert Israel, <a href="/A257762/b257762.txt">Table of n, a(n) for n = 1..10000</a>
%e A257762 a(1) = A258437(A258432(2)) = 1.
%p A257762 Primes:= select(isprime,[2,(2*i+1 $ i=1..10^4)]):
%p A257762 Gaps:= Primes[2..-1] - Primes[1..-2]:
%p A257762 G2:= Gaps[2..-1] - 2*Gaps[1..-2]:
%p A257762 ListTools:-SearchAll(0,G2); # _Robert Israel_, May 22 2015
%t A257762 Select[Range@ 600, 2 Prime[#] - Prime[# + 1] == 2 Prime[# + 1] - Prime[# + 2] &] (* _Michael De Vlieger_, May 11 2015 *)
%o A257762 (Magma) [n: n in [0..600] | 2*NthPrime(n)-NthPrime(n+1) eq 2*NthPrime(n+1)-NthPrime(n+2)]; // _Vincenzo Librandi_, May 12 2015
%o A257762 (Haskell)
%o A257762 a257762 n = a257762_list !! (n-1)
%o A257762 a257762_list = map a258432 $ filter ((== 2) . a258383) [1..]
%o A257762 -- _Reinhard Zumkeller_, May 31 2015
%Y A257762 Cf. A258383, A258432, A258437, A258469, A257762, A258449, A257892, A257951.
%K A257762 nonn
%O A257762 1,2
%A A257762 _Zak Seidov_, May 07 2015