This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(n)=v=[1];k=1;while(#v<=n,if(isprime(k+v[#v])&&!vecsearch(vecsort(v),k),v=concat(v,k);k=0);k++);v[#v-1] n=1;while(n<1000,if(a(n)==n,print1(n,", "));n++) \\ Derek Orr, Jun 08 2015
import Data.List (elemIndex) import Data.Maybe (fromJust) a117922 = (+ 1) . fromJust . (`elemIndex` a055265_list) -- Reinhard Zumkeller, Feb 14 2013
A282695 := proc(n) A055265(n)-n ; end proc: seq(A282695(n),n=1..100) ; # R. J. Mathar, Feb 25 2017
S:= {1}: L:= {}:
a[1]:= 1: b[1]:= 1:
count:= 1:
for n from 2 to 10000 do
for k in L do
if isprime(k+b[n-1]) then
b[n]:= k;
S:= S union {k};
L:= L minus {k};
if L = {} then
count:= count+1;
a[count]:= n;
fi;
break;
fi
od:
if not assigned(b[n]) then
for k from max(S) + 1 do
if isprime(k+b[n-1]) then
b[n]:= k;
if k = max(S) + 1 and L = {} then
count:= count+1;
a[count]:= n;
fi;
S:= S union {k};
L:= {$1..k} minus S;
break
fi
od
fi;
od:
seq(a[i], i=1..count); # Robert Israel, Sep 10 2014
A282696 := proc() local r,i,a282695; r := -1 ; for i from 1 do a282695 := abs(A282695(i)) ; if a282695 > r then r := a282695 ; printf("%d,\n",i) ; end if; end do: end proc: A282696() ; # R. J. Mathar, Apr 30 2017
We start with a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 3, the smallest possibilities which do not lead to a contradiction. Indeed, the four sums 0 + 2, 0 + 3, 1 + 2 and 2 + 3 are prime.
Now we have 2 prime sums using {1, 2, 3}, so the next term must give two more prime when added to these. We find that a(4) = 4 is the smallest possible choice, with 1 + 4 = 5 and 3 + 4 = 7.
Then there are again 2 primes among the pairwise sums using {2, 3, 4}, so the next term must again produce two more prime sums. We find that a(5) = 9 is the smallest possibility, with 2 + 9 = 11 and 4 + 9 = 13.
a(10^4) = 9834 and all numbers up to 9834 occurred by then.
a(10^5) = 99840 and all numbers below 99777 occurred by then.
a(10^6) = 1000144 and all numbers below 999402 occurred by then.
A329449(n, show=0, o=0, N=4, M=3, p=[], U, u=o)={for(n=o, n-1, if(show>0, print1(o", "), show<0, listput(L,o)); U+=1<<(o-u); U>>=-u+u+=valuation(U+1, 2); p=concat(if(#p>=M, p[^1], p), o); my(c=N-sum(i=2, #p, sum(j=1, i-1, isprime(p[i]+p[j])))); for(k=u, oo, bittest(U, k-u) || min(c-#[0|p<-p, isprime(p+k)], #p>=M) || [o=k, break]));show&&print([u]); o} \\ Optional args: show=1: print a(o..n-1), show=-1: append a(o..n-1) to the global list L, in both cases print [least unused number] at the end; o=1: start with a(1)=1; N, M: get N primes using M+1 consecutive terms.
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