A351318 a(n) is the least prime prime(k), k > n, such that A036689(k) or A036690(k) is s(n) + s(n+1) + ... + s(j), j < k, where each s(i) is either A036689(i) or A036690(i)

3, 7, 13, 31, 47, 47, 53, 53, 73, 137, 103, 131, 109, 137, 239, 257, 229, 349, 257, 269, 331, 347, 389, 409, 257, 389, 251, 229, 499, 487, 509, 491, 541, 487, 353, 739, 571, 743, 727, 307, 883, 743, 929, 827, 971, 911, 887, 569, 1063, 751, 1013, 883, 1451, 977, 1259, 853, 983, 947, 967, 1049

Offset

1,1

Comments

a(n) is the least prime p such that p*(p-1) or p*(p+1) is the sum of a sequence where each term is either prime(i)*(prime(i)-1) or prime(i)*(prime(i)+1), for i from n to some j.

Links

Robert Israel, Table of n, a(n) for n = 1..2400

Example

a(3) = 13 because prime(3) = 5, the next two primes are 7 and 11, and 5*6 + 7*6 + 11*10 = 182 = 13*14.

Maple

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):
R:= convert(map(p -> (p*(p-1), p*(p+1)), P), set):
f:= proc(n) local S, T, SR, i, s;
  S:= {P[n]*(P[n]-1), P[n]*(P[n]+1)};
  for i from n+1 do
    T:= [P[i]*(P[i]-1), P[i]*(P[i]+1)];
    S:= map(s -> (s+T[1], s+T[2]), S);
    SR:= S intersect R;
    if SR <> {} then
        s:= (sqrt(1+4*min(SR))-1)/2;
      if isprime(s) then return s else return s+1 fi
    fi
  od
end proc:
map(f, [$1..100]);

Crossrefs

Cf. A036889, A036890.

Sequence in context: A163418 A309738 A161218 * A068679 A006978 A060424

Adjacent sequences: A351315 A351316 A351317 * A351319 A351320 A351321

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 18 2022

Status

approved