cp's OEIS Frontend

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.

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).

Original entry on oeis.org

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

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Author

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

Keywords

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.

Examples

			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.
		

Crossrefs

Programs

  • 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]);