A073660 -id:A073660 - cp's OEIS frontend

A073659 a(1) = 1; for n > 1, a(n) is the smallest even number not already in the sequence such that a(1) + ... + a(n) is a prime.

1, 2, 4, 6, 10, 8, 12, 16, 14, 24, 30, 22, 18, 26, 34, 36, 20, 28, 38, 40, 32, 42, 46, 48, 44, 52, 56, 60, 54, 58, 66, 50, 64, 62, 70, 84, 90, 72, 92, 76, 86, 94, 74, 88, 68, 82, 80, 102, 96, 100, 114, 98, 78, 112, 120, 110, 108, 106, 126, 122, 130, 132, 134, 124, 128, 118

Offset: 1

Amarnath Murthy, Aug 10 2002

Essentially the same as A054408. - R. J. Mathar, Dec 15 2008

Conjecture: Every even number appears. - N. J. A. Sloane, May 29 2017

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..4097 from N. J. A. Sloane).

Cf. A054408, A073660.

See A055265 for a version where the sums of two adjacent terms are primes.

t = {1}; Do[i = 2; While[! PrimeQ[Total[t] + i] || MemberQ[t, i], i += 2]; AppendTo[t, i], {65}]; t (* Jayanta Basu, Jul 04 2013 *)

v=[1];n=1;while(n<200,if(isprime(n+vecsum(v))&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ Derek Orr, Jun 01 2015

More terms from Sascha Kurz, Jan 28 2003

Offset corrected by Chai Wah Wu, Aug 27 2017

A075574 a(1) = 1, then the smallest number (obviously even) greater than the previous term such that every partial sum is prime.

Original entry on oeis.org

1, 2, 4, 6, 10, 14, 16, 18, 26, 30, 36, 48, 52, 54, 56, 58, 60, 66, 74, 78, 88, 90, 96, 104, 106, 108, 122, 126, 144, 154, 156, 158, 172, 188, 190, 192, 206, 210, 214, 228, 240, 242, 250, 258, 260, 262, 284, 286, 288, 290, 298, 300, 302, 318, 324, 328, 332, 340

Offset: 1

Amarnath Murthy, Sep 25 2002

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A073659, A073660.

A075574:=proc(n) local i,j,k,t,s; j:=1; s:=1; t:=1; for i to n do k:=s; s:=nextprime(s+j); j:=s-k; t:=t,j; od; t; end; # Floor van Lamoen, Oct 21 2005

nxt[{ps_,a_}]:=Module[{c=a+2},While[!PrimeQ[ps+c],c+=2];{ps+c,c}]; Join[ {1},NestList[nxt,{3,2},60][[All,2]]] (* Harvey P. Dale, Sep 19 2021 *)

More terms from David Wasserman, Jan 20 2005

cp's OEIS Frontend

A073659 a(1) = 1; for n > 1, a(n) is the smallest even number not already in the sequence such that a(1) + ... + a(n) is a prime.

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