A128933 A103828(n) + 1.
2, 4, 10, 28, 70, 430, 1060, 56500, 166840, 5020060, 7681810, 274343590, 8316187180
Offset: 1
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(5) = 38 because 38+2+1, 38+4+1, 38+8+1 and 38+14+1 are all prime.
a093483 n = a093483_list !! (n-1)
a093483_list = f ([2..7] ++ [8,14..]) [] where
f (x:xs) ys = if all (== 1) $ map (a010051 . (+ x)) ys
then x : f xs ((x+1):ys) else f xs ys
-- Reinhard Zumkeller, Dec 11 2011
EP:=[2,4]: P:=[]: for w to 1 do for n from 1 to 800*10^6 do s:=6*n+2; Q:=map(z-> z+s+1); if andmap(isprime,Q) then EP:=[op(EP),s]; P:=[op(P),op(Q)] fi; od od; EP; P: # Walter Kehowski, Jun 03 2006
f[1] = 2; f[2] = 4; f[3] = 8; f[n_] := f[n] = Block[{lst = Array[f, n - 1], k = f[n - 1] + 7}, While[ Union[ PrimeQ[k + lst]] != {True}, k += 6]; k-1]; Array[f, 13] (* Robert G. Wilson v, Oct 16 2012 *)
The pairwise averages of {3,7,19} are the primes {5,11,13}.
The pairwise averages of first three terms in A115760, {3,7,19} produce the set of primes {5,11,13}.
4+54+1 is prime.
a(6)=27 because it is the smallest number producing 3 primes in the sums with all previous terms: a(1)+27 = 2+27 = 29, a(3)+27 = 4+27 = 31, a(5)+27 = 10+27 = 37; a(7)=34: a(2)+34 = 3+34 = 37, a(4)+34 = 9+34 = 43, a(6)+34 = 27+34 = 61; a(8)=69 because it is the smallest number producing 4 primes in the sums with all previous terms: a(1)+69 = 2+69 = 71, a(3)+69 = 4+69 = 73, a(5)+69 = 10+69 = 79, a(7)+69 = 34+69 = 103.
PT(x)={print1(x,", ");write("b291163.txt",n++," ",x)};
n=0;
ae=vector(11);
ao=vector(11);
ae[1]=2;PT(ae[1]);
ao[1]=3;PT(ao[1]);
for (m=1,10,\
start=(ao[m]+1)/2;\
for (kh=start,100*start,k=kh+kh;\
for(jj=1,m,j=m-jj+1;if(!isprime(k+ao[j]),next(2)));\
ae[m+1]=k;PT(k);break(1));\
start=ae[m+1]/2;\
for (kh=start,100*start,k=kh+kh+1;\
for(jj=1,m+1,j=m-jj+2;if(!isprime(k+ae[j]),next(2)));\
ao[m+1]=k;PT(k);break(1)))
\\ Hugo Pfoertner, Oct 10 2017
a(2)=4 since 4 is the first even number > a(1)=2 such that 2*4-1=7 is prime and 4+2-1=5 is prime.
EP:=[2]: for w to 1 do for k from 0 to 12^8 do n:=6*k+4; p:=2*n-1; Q:=map(z-> z+n-1, EP); if isprime(p) and andmap(isprime,Q) then EP:=[op(EP),n]; print(n); fi od od;
a(2)=9 since 9 is the first odd number > a(1)=3 such that 2*9-1=17 is prime and 9+3-1=13 is prime.
OP:=[3]: for w to 1 do for k from 0 to 12^8 do n:=6*k+3; p:=2*n-1; Q:=map(z-> z+n-1, OP); if isprime(p) and andmap(isprime,Q) then OP:=[op(OP), n]; print(n); fi od od;
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