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A243625
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a(n) is the smallest positive integer not already in the sequence for which a(n)+a(n-1) is a semiprime, with a(1)=1.
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8
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1, 3, 6, 4, 2, 7, 8, 13, 9, 5, 10, 11, 14, 12, 21, 17, 16, 18, 15, 19, 20, 26, 23, 28, 27, 22, 24, 25, 30, 32, 33, 29, 36, 38, 31, 34, 35, 39, 43, 42, 40, 37, 45, 41, 44, 47, 46, 48, 58, 53, 62, 49, 57, 54, 52, 59, 56, 50, 61, 60, 51, 55, 63, 66, 67, 74, 68
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OFFSET
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1,2
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COMMENTS
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It is probable that every positive integer occurs, and that this is a permutation of natural numbers.
a(n) = n for n = 1, 4, 9, 18, 23, 48, 54, 60, 63, 77, 91, 92, .... (375 cases for first 3000 terms). - Zak Seidov, Feb 22 2017
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LINKS
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EXAMPLE
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a(3)=6 because 1 and 3 have already been used in the sequence and 3+2=5, 3+4=7 and 3+5=8 are not semiprime while 3+6=9 is semiprime.
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MAPLE
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N:= 1000; # to get all terms up to a(N)
issp:= proc(n) local F; F:= ifactors(n)[2]; add(f[2], f=F)=2 end proc:
S:= {1}; m:= 1; R:= {}; a[1]:= 1;
for n from 2 to N do
found:= false;
for k in R do
if issp(a[n-1]+k) then
a[n]:= k;
S:= S union {k};
R:= R minus {k};
found:= true;
break
fi;
od;
if not found then
for k from m+1 do
if issp(a[n-1]+k) then
a[n]:= k;
S:= S union {k};
R:= R union {$(m+1)..(k-1)};
m:= k;
break
fi
od
fi
od:
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MATHEMATICA
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f[s_List] := Block[{k = 1, a = s[[ -1]]}, While[ MemberQ[s, k] || ! Plus@@Last/@FactorInteger[a+k] == 2, k++ ]; Append[s, k]]; Nest[f, {1}, 71]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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