A376115 Least common differences in the arithmetic progressions corresponding to A376109.
1, 1, 1, 1, 2, 2, 2, 1, 3, 1, 4, 4, 2, 4, 1, 1, 6, 6, 6, 2, 6, 8, 6, 8, 3, 11, 7, 8, 6, 2, 12, 1, 12, 12, 1, 12, 6, 12, 1, 4, 12, 12, 12, 16, 1, 12, 18, 16, 14, 5, 13, 22, 12, 14, 17, 16, 11, 12, 6, 4, 24, 24, 18, 1, 7, 24, 24, 24, 18, 2, 12, 24, 6, 35, 5, 13, 19, 33, 6, 8, 21, 24, 12, 24, 8, 24
Offset: 1
Keywords
Examples
a(7) = 2 because the arithmetic progression 3, 5, 7 of A376109(7) = 3 primes ending in 7 has common difference of 5 - 3 = 7 - 5 = 2. There are two arithmetic progressions of semiprimes of A376109(14) = 3 ending in 14, namely 6, 10, 14 with common difference 4 and 4, 9, 14 with common difference 5, so a(14) = 4.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
M:= Array(1..10): for n from 2 to 100 do v:= numtheory:-bigomega(n); if M[v] = 0 then M[v]:= n else M[v]:= M[v], n fi; od: for i from 1 to 10 do M[i]:= [M[i]] od: f:= proc(s) local n,i,m,d,v,j,dm; m:= 1; dm:= 1; v:= numtheory:-bigomega(s); member(s,M[v],n); for i from n-1 to 1 by -1 do d:= s - M[v][i]; if s - m*d < M[v][1] then return dm fi; for j from 2 while ListTools:-BinarySearch(M[v],s-j*d) <> 0 do od: if j > m then m:= j; dm:= d fi; od; dm; end proc: f(1):= 1: map(f, [$1..100]);
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