A332941 Lexicographically earliest sequence of positive numbers in which no set of consecutive terms sums to a prime.

1, 8, 1, 15, 9, 1, 14, 6, 30, 6, 9, 15, 6, 4, 8, 12, 10, 14, 6, 12, 8, 10, 12, 18, 12, 6, 6, 6, 24, 6, 6, 8, 1, 9, 6, 10, 8, 12, 6, 14, 10, 6, 4, 8, 12, 10, 20, 6, 18, 6, 6, 4, 8, 12, 6, 4, 12, 8, 10, 8, 6, 6, 18, 6, 6, 20, 10, 12, 8, 4, 6, 12, 12, 6, 12, 6, 12

Offset: 1

Author

S. Brunner, Mar 03 2020

Keywords

• nonn

Comments

Terms >= 30 seem to be very rare. Up to a(450000), 30 appears only 7 times: at n = 9, 288, 2507, 15902, 54405, 242728, 425707.

For n <= 450000, the largest term is 32; it appears at n = 335308 and 370687.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A254337, A084833.

Programs

Maple

s:= proc(i, j) option remember; `if`(i>j, 0, a(j)+s(i, j-1)) end:
a:= proc(n) option remember; local k; for k while
      ormap(isprime, [k+s(i, n-1)$i=1..n]) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 23 2020

Mathematica

s[i_, j_] := s[i, j] = If[i > j, 0, a[j] + s[i, j-1]];
a[n_] := a[n] = Module[{k}, For[k = 1, AnyTrue[k+Table[s[i, n-1], {i, 1, n}], PrimeQ], k++]; k];
Array[a, 100] (* Jean-François Alcover, Nov 17 2020, after Alois P. Heinz *)

Python

def A(ee):
    a=[1]
    print(1)
    n=1
    while n<=ee:
        i=1
        while i>0:
            ii=i
            iz=c=0
            while iz<=len(a):
                c=0
                if ii>2:
                    for j in range(2, int((ii)**0.5+1.5)):
                        if ii%j==0:
                            c=1
                            break
                if c==0 and ii>1:
                    break
                else:
                    iz += 1
                    ii=ii+a[n-iz]
            if c==1:
                n += 1
                a.append(i)
                print(i)
                break
            if i<4:
                i=4
            else:
                i += 1
    return a