A070026 Initial, all intermediate and final iterated sums of digits of n are primes.

2, 3, 5, 7, 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41, 43, 47, 50, 52, 56, 61, 65, 70, 74, 83, 92, 101, 102, 104, 106, 110, 111, 113, 115, 119, 120, 122, 124, 128, 131, 133, 137, 140, 142, 146, 151, 155, 160, 164, 173, 182, 191, 200, 201, 203, 205, 209, 210, 212, 214, 218

Offset

1,1

Comments

2999 = A062802(4) is the smallest term of this sequence for which the second iterated sum of digits is not the final sum; i.e. the smallest requiring three summations (2+9+9+9=29, 2+9=11, 1+1=2 and all three sums are prime). (The corresponding statement about the very large A062802(5) is not true because a large number of smaller nonprimes of the same digit length also have the digit sum 2999, the least being 29999..., where 333 9's follow the 2.). A062802, a sequence of primes, is a subsequence of this sequence and of A070027.

Additional terms can be generated by finding the next number whose digit sum is a prime already in the sequence. - Felix Fröhlich, Jun 13 2014

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

47 is here because 4+7=11 and 11 is prime while also 1+1=2 and 2 is prime. 39 (in A028835) is not a term: 3+9=12 is not prime - although 1+2=3 is prime. 49 (in A028834) is not a term: 4+9=13 is prime but 1+3=4 is not prime.

Crossrefs

Cf. A028834 (Initial sum is prime), A028835 (Final sum is prime), A062802, A070027 (Primes from this sequence).

Sequence in context: A307895 A028835 A028834 * A139750 A330125 A139749

Adjacent sequences: A070023 A070024 A070025 * A070027 A070028 A070029

Keyword

base,easy,nonn

Author

Rick L. Shepherd, Apr 13 2002

Extensions

Terms corrected by Felix Fröhlich, Jun 13 2014

Status

approved