A080355 a(1)=1; thereafter, a(n+1) = a(n) + 2^(prime(n)-1).

1, 3, 7, 23, 87, 1111, 5207, 70743, 332887, 4527191, 272962647, 1346704471, 70066181207, 1169577808983, 5567624320087, 75936368497751, 4579535995868247, 292809912147579991, 1445731416754426967, 75232707711592633431, 1255824328429003936855, 5978190811298649150551

Offset

1,2

Comments

Original name: a(1)=1; for n>1, a(n) = a(n-1) + 2^(j-1), where j = prime(n-1) is position of n-th 1 in A080339.

Or, take an initial segment of A080339, stopping at the n-th 1, reverse and interpret as a binary number. E.g., to get the 4th term: 11101 -> 10111 = 23, so a(4) = 23.

Indices of noncomposite terms in the sequence are 1, 2, 3, 4, 9, 310, 418, .... Next term (i.e., index of a prime), if it exists, is > 2000. See also post to SeqFan list by Tomasz Ordowski. - M. F. Hasler, Oct 30 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..475

Tomasz Ordowski, Primes in primes, SeqFan list, Oct 28 2018.

Formula

a(n) = 1 + Sum_{k=1..n-1} 2^(prime(k)-1).

a(n) = A076793(n-1) / 2 + 1. - Georg Fischer, Aug 12 2023

Maple

a:=n->1+add(2^(ithprime(k)-1), k=1..n-1): seq(a(n), n=1..25); # Muniru A Asiru, Oct 31 2018

Mathematica

RecurrenceTable[{a[1]==1, a[n] == 2^(Prime[n-1] - 1) + a[n-1]}, a, {n, 25}] (* Vincenzo Librandi, Oct 31 2018 *)
nxt[{n_, a_}]:={n+1, a+2^(Prime[n]-1)}; NestList[nxt, {1, 1}, 30][[All, 2]] (* Harvey P. Dale, Aug 07 2019 *)

Prog

(PARI) apply( A080355(n)=1+sum(i=1, n-1, 2^(prime(i)-1)), [1..50]) \\ M. F. Hasler, Oct 30 2018
(Magma) [n le 1 select 1 else Self(n-1) + 2^(NthPrime(n-1)-1): n in [1..25]]; // Vincenzo Librandi, Oct 31 2018

Crossrefs

Cf. A076793.

Sequence in context: A099152 A289317 A113860 * A366694 A100964 A080077

Adjacent sequences: A080352 A080353 A080354 * A080356 A080357 A080358

Keyword

nonn,easy

Author

N. J. A. Sloane, based on information supplied by Artur Jasinski, Mar 21 2003

Extensions

More terms from Vladeta Jovovic, Mar 26 2003

Status

approved