A362720 a(n) is the smallest k > 0 such that b(n) = b(n-1) + A007504(k) is prime, with b(0) = 1.

1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 41, 3, 1, 5, 1, 3, 1, 11, 33, 3, 57, 17, 7, 17, 5, 17, 9, 17, 9, 1, 9, 1, 3, 1, 5, 1, 5, 17, 9, 17, 5, 17, 5, 65, 11, 17, 3, 33, 9, 33, 7, 35, 7, 33, 9, 1, 5, 1, 3, 1, 9, 17, 5, 1, 5, 41, 21, 33, 9, 1, 3, 33, 21, 1, 9, 33, 3

Offset

1,4

Comments

Regarding the most common values seen, through 15 million terms, value 3 is seen 1065490 times, value 17 is seen 1085824 times. These two values correspond to A007504(3)=10 and A007504(17)=440. Will these two values continue to be the most frequent? If so, why?

Links

Table of n, a(n) for n=1..77.

Example

We label the corresponding prime sequence b(*).  So, b(1) = b(0) + 2 is prime, so a(1) = 1 giving b(1) = 3. Later b(10) = 53, so that b(11) = b(10) + 3266 is the earliest prime, so a(11)=41 (via A007504(41)).

Prog

(PARI) genit(nterms=50)={my(arr=List(), last=1, summ, icnt); while(#arr<nterms, summ=last; icnt=0; forprime(x=2, +oo, summ+=x; icnt+=1; if(icnt%2==0, next); if(ispseudoprime(summ), listput(arr, icnt); last=summ; break))); arr}

Crossrefs

Cf. A007504.

Sequence in context: A330889 A035652 A359943 * A205526 A233269 A035689

Adjacent sequences: A362717 A362718 A362719 * A362721 A362722 A362723

Keyword

nonn,easy

Author

Bill McEachen, Apr 30 2023

Status

approved