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Least multiple of n that is the sum of 2 successive primes.
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%I #25 Oct 06 2021 10:08:15

%S 5,8,12,8,5,12,42,8,18,30,198,12,52,42,30,112,68,18,152,60,42,198,138,

%T 24,100,52,162,84,696,30,186,128,198,68,210,36,222,152,78,120,410,42,

%U 172,308,90,138,564,144,882,100,204,52,1272,162,330,112,456,696,472,60,1220,186,630,128,390

%N Least multiple of n that is the sum of 2 successive primes.

%C a(n) = n if n is a term of A001043 (on graph this corresponds to the lower bound).

%H Michel Marcus, <a href="/A247245/b247245.txt">Table of n, a(n) for n = 1..10000</a>

%H Zak Seidov, <a href="/A247245/a247245.txt">Table of {n, i, a(n), k=a(n)/n} for n = 1..1000</a>

%F a(n) = smallest number, of the form k*n (k >= 1), that is the sum of 2 successive primes.

%e 5 is a term because prime(1) + prime(2) = 2 + 3 = 5 = 5*1 (k = 5),

%e 8 is a term because prime(2) + prime(3) = 3 + 5 = 8 = 4*2 (k = 4),

%e 198 is a term because prime(25) + prime(26) = 97 + 101 = 198 = 18*11 (k = 18).

%o (PARI) is(n) = (precprime((n-1)/2) + nextprime(n/2) == n) && (n>2); \\ A001043

%o a(n) = my(k=1); while (!is(k*n), k++); k*n; \\ _Michel Marcus_, Oct 06 2021

%Y Cf. A001043.

%K nonn

%O 1,1

%A _Zak Seidov_, Nov 28 2014