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A268035 a(n) is the smallest integer m such that each of the numbers m, 2*m, 3*m, ..., n*m is the sum of two successive primes. 0

%I #14 Feb 11 2016 10:43:26

%S 5,12,12,30,120,1036350,19714254,318409146,2281029060

%N a(n) is the smallest integer m such that each of the numbers m, 2*m, 3*m, ..., n*m is the sum of two successive primes.

%C If exactly n multiples were requested, then a(2) would be 18. - _Michel Marcus_, Jan 25 2016

%e a(4)=30 because each of the numbers 30, 60, 90, and 120 is the sum of 2 successive prime numbers: 13+17=30, 29+31=60, 43+47=90, and 59+61=120.

%t Table[m = 1; While[! AllTrue[m Range@ n, Function[m, If[PrimeQ@ #, # + NextPrime@ #, NextPrime@ # + NextPrime[#, -1]] == m &@((m - 1)/2)]], m++]; m, {n, 5}] (* _Michael De Vlieger_, Jan 27 2016 *)

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

%o isok(m,n) = {for (k=1, n, if (! is(m*k), return (0));); return(1);}

%o a(n) = {my(j=1); while (! isok(j,n), j++); j;} \\ _Michel Marcus_, Jan 25 2016

%Y Each term belongs to A001043.

%K nonn,more

%O 1,1

%A _David Radcliffe_, Jan 24 2016

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