A203075 -id:A203075 - cp's OEIS frontend

A203076 Convert A203075(n) to base 10.

0, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 26, 27, 29, 30, 31, 39, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 58, 59, 61, 62, 63, 67, 69, 70, 71, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 90, 91, 93, 94, 95

Offset: 0

Frank M Jackson and N. J. A. Sloane, Dec 28 2011

nonn

Any nonnegative number can be written as a sum of distinct terms of the complete sequence, A203074. Terms a(n) are decimal representations of binary vectors (in ascending powers of 2) used to select terms of A203074 that when summed give n.

Wikipedia, "Complete" sequence. [Wikipedia calls a sequence "complete" (sic) if every positive integer is a sum of distinct terms. This name is extremely misleading and should be avoided. - _N. J. A. Sloane_, May 20 2023]

Cf. A203074, A203075.

nextprime[n_Integer] := (k=n+1;While[!PrimeQ[k], k++];k);aprime[m_Integer] := (If[m==0, 1, nextprime[2^(m-1)]]);seqtable[l_] := (stable=Table[aprime[j], {j, 0, l}];stable);inttable[p_] := (itable=Reverse[IntegerDigits[p, 2]];itable);h=1;otable={0};ttable={};While[h<100, (inttable[h];seqtable[Length[itable]-1];test=itable.stable;If[!MemberQ[ttable, test], AppendTo[otable, h], Null];AppendTo[ttable, test];h++)];otable

Binary(a(n)) x A203074 = n, where x is the inner product and the binary vector is in ascending powers of 2 with infinite trailing zeros.

A203074 a(0)=1; for n > 0, a(n) = next prime after 2^(n-1).

Original entry on oeis.org

1, 2, 3, 5, 11, 17, 37, 67, 131, 257, 521, 1031, 2053, 4099, 8209, 16411, 32771, 65537, 131101, 262147, 524309, 1048583, 2097169, 4194319, 8388617, 16777259, 33554467, 67108879, 134217757, 268435459, 536870923, 1073741827, 2147483659

Offset: 0

Frank M Jackson and N. J. A. Sloane, Dec 28 2011

nonn

Equals {1} union A014210. Unlike A014210, every positive integer can be written in one or more ways as a sum of terms of this sequence. See A203075, A203076.

a(n)*2^(n-1) = A133814(n-1) for n > 1 and a(n)*2^(n-1) for n > O is a subsequence of primitive practical numbers (A267124). - Frank M Jackson, Dec 29 2024

			a(5) = 17, since this is the next prime after 2^(5-1) = 2^4 = 16.

M. F. Hasler & Bill McEachen, Table of n, a(n) for n = 0..1300 (missing lines n = 1159..1165 from Bill McEachen)
Wikipedia, "Complete" sequence. [Wikipedia calls a sequence "complete" (sic) if every positive integer is a sum of distinct terms. This name is extremely misleading and should be avoided. - _N. J. A. Sloane_, May 20 2023]

Cf. A013632, A013597, A014210, A104080, A203075, A203076.

[1] cat [NextPrime(2^(n-1)): n in [1..40]]; // Vincenzo Librandi, Feb 23 2018

nextprime[n_Integer] := (k=n+1;While[!PrimeQ[k], k++];k); aprime[m_Integer] := (If[m==0, 1, nextprime[2^(m-1)]]); Table[aprime[l], {l,0,100}]
nxt[{n_,a_}]:={n+1,NextPrime[2^n]}; NestList[nxt,{0,1},40][[All,2]] (* Harvey P. Dale, Oct 10 2017 *)

a(n)=if(n,nextprime(2^n/2+1),1) \\ Charles R Greathouse IV

A203074(n)=nextprime(2^(n-1)+1)-!n  \\ M. F. Hasler, Mar 15 2012

A203074(n) = 2^(n-1) + A013597(n-1), for n > 0. - M. F. Hasler, Mar 15 2012

a(n) = A104080(n-1) for n > 2. - Georg Fischer, Oct 23 2018

cp's OEIS Frontend

A203076 Convert A203075(n) to base 10.

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