A157715 Primes sorted on digit sums, then on the primes.

2, 11, 101, 3, 13, 31, 103, 211, 1021, 1201, 2011, 3001, 10111, 20011, 20101, 21001, 100003, 102001, 1000003, 1011001, 1020001, 1100101, 2100001, 10010101, 10100011, 20001001, 30000001, 101001001, 200001001, 1000000021, 1000001011

Offset

1,1

Comments

Beyond n = 4, a(n) is believed to coincide with A062339.

Only correct for n >= 4 if an undiscovered prime of digit sum two (which would have to be a member of A080176) does not exist; this is conjectured but not proved. - Jeppe Stig Nielsen, Mar 30 2018

Links

Table of n, a(n) for n=1..31.

Example

There are only three primes with a digit sum of 2, and those are 2, 11, 101. Therefore these three primes are the first three terms of this sequence.
There is only one prime with a digit sum of 3, and that's 3 itself. Any higher number with a digit sum of 3 is a nontrivial multiple of 3 and therefore composite.
Then follows the first prime with a digit sum of 4, which is 13.

Mathematica

Prime@ Flatten@ Values@ Take[KeySort@ PositionIndex[Total@ IntegerDigits@ # & /@ Prime@ Range[10^7]], 3] (* Michael De Vlieger, Apr 07 2018 *)

Crossrefs

Cf. A062341.

Sequence in context: A318007 A243950 A056732 * A001271 A038371 A236174

Adjacent sequences: A157712 A157713 A157714 * A157716 A157717 A157718

Keyword

nonn,base

Author

Lekraj Beedassy, Mar 04 2009

Extensions

Comment edited by Robert Israel, Dec 28 2015

Status

approved