A385988 -id:A385988 - cp's OEIS frontend

A386905 Distinct terms in A385988.

1, 2, 3, 7, 23, 11415, 56553873808298479843537432588765043239809588104012779518849306976361095532563320075112688420502361617080665176812695

Offset: 1

Paolo Xausa and David A. Corneth, Aug 07 2025

nonn

David A. Corneth, PARI program

Cf. A385988.

s = 0; k = 1; Reap[Do[s += k; If[IntegerQ@ Log2[s], k = n; Sow[k]], {n, 2^16}] ][[-1, 1]] (* Michael De Vlieger, Aug 07 2025 *)

PARI
```
\\ See Corneth link
```

A385986 a(1) = 2, and for any n > 1, a(n) is the largest k < n such that a(1) + ... + a(k) is prime.

Original entry on oeis.org

2, 1, 2, 3, 3, 5, 5, 5, 5, 9, 9, 9, 9, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 65, 65, 65

Offset: 1

Rémy Sigrist, Jul 14 2025

In other words: a(1) = 2, and for any n > 0, if a(1) + ... + a(n) is prime then a(n+1) = n, otherwise a(n+1) = a(n).

This sequence is unbounded: for any n > 1, let P = a(1) + ... + a(a(n)); P is prime and a(a(n)+1) = a(n); as P > a(n), P and a(n) are coprime, hence, by Dirichlet's theorem on arithmetic progressions, P + k*a(n) is prime for some minimal k > 0, and a(a(n)+k+1) = a(n)+k > a(n).

			Sequence begins:
  n   a(n)  a(1)+...+a(n)  Prime?
  --  ----  -------------  ------
   1     2              2  Yes
   2     1              3  Yes
   3     2              5  Yes
   4     3              8  No
   5     3             11  Yes
   6     5             16  No
   7     5             21  No
   8     5             26  No
   9     5             31  Yes
  10     9             40  No
  11     9             49  No
  12     9             58  No
  13     9             67  Yes
  14    13             80  No

Rémy Sigrist, Table of n, a(n) for n = 1..10000

See A385988 and A386369 for similar sequences.

Cf. A385987 (corresponding prime numbers).

v = 2;t = 0;values={};Do[AppendTo[values,v];t+=v;If[PrimeQ[t],v=n],{n, 1, 68}];values (* James C. McMahon, Jul 22 2025 *)

{ v = 2; t = 0; for (n = 1, 68, print1 (v", "); if (isprime(t += v), v = n);); }

cp's OEIS Frontend

A386905 Distinct terms in A385988.

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