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A270267 Carmichael numbers (A002997) that are the sum of three consecutive primes. 2

%I #26 Jun 25 2019 11:55:44

%S 252601,410041,1615681,2113921,10606681,10877581,11921001,26932081,

%T 44238481,54767881,82929001,120981601,128697361,208969201,246446929,

%U 255160621,278152381,280067761,311388337,325546585,334783585,416964241,533860309,593234929,672389641

%N Carmichael numbers (A002997) that are the sum of three consecutive primes.

%C In other words, Carmichael numbers of the form p + q + r where p, q and r are consecutive primes.

%C If a Carmichael number is the sum of n consecutive primes, it is so obvious that the minimum value of n is 3.

%C Intersection of A002997 and A034961.

%H Amiram Eldar, <a href="/A270267/b270267.txt">Table of n, a(n) for n = 1..10000</a>

%e 84191, 84199 and 84211 are consecutive primes and sum of them is 252601 that is a Carmichael number.

%e 136657, 136691 and 136693 are consecutive primes and sum of them is 410041 that is a Carmichael number.

%e 538553, 538561 and 538567 are consecutive primes and sum of them is 1615681 that is a Carmichael number.

%o (PARI) isA002997(n) = {my(f); bittest(n, 0) && !for(i=1, #f=factor(n)~, (f[2, i]==1 && n%(f[1, i]-1)==1)||return) && #f>1}

%o a034961(n) = my(p=prime(n), q=nextprime(p+1)); p+q+nextprime(q+1);

%o for(n=1, 1e6, if(isA002997(a034961(n)), print1(a034961(n), ", ")));

%Y Cf. A002997, A034961.

%K nonn

%O 1,1

%A _Altug Alkan_, Mar 14 2016

%E More terms from _Amiram Eldar_, Jun 25 2019

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)