A341696 The cumulative sum (1st digit + 2nd digit + 3rd digit + ... + n-th digit of the sequence) is prime.

2, 1, 4, 6, 40, 20, 46, 8, 42, 400, 60, 62, 64, 26, 406, 80, 48, 4000

Offset

1,1

Comments

This is the lexicographically earliest sequence of distinct terms > 0 with the property. The sequence stops after a(18) = 4000 as the cumulative sum is 113 at that point and the next prime (127) is impossible to reach with a single digit.

Links

Table of n, a(n) for n=1..18.

Example

2 is prime, and so are the successive digit sums (2+1=3), (2+1+4=7), (2+1+4+6=13), (2+1+4+6+4=17), (2+1+4+6+4+0=17), (2+1+4+6+4+0+2=19), (2+1+4+6+4+0+2+0=19), etc.

Mathematica

s = {}; sum = 0; Do[k = 1; While[MemberQ[s, k] || !AllTrue[(sumd = Accumulate @ IntegerDigits[k]), PrimeQ[sum + #] &], k++]; AppendTo[s, k]; sum += sumd[[-1]], {18}]; s (* Amiram Eldar, Feb 17 2021 *)

Crossrefs

Cf. A001223 (prime gaps).

Sequence in context: A145858 A328491 A328357 * A052566 A234946 A223092

Adjacent sequences: A341693 A341694 A341695 * A341697 A341698 A341699

Keyword

base,nonn,fini,full

Author

Eric Angelini, Feb 17 2021

Status

approved