A386475 Least prime starting a run of exactly n consecutive primes with identical counts of odd digits.

2, 5, 3, 11, 97, 503, 499, 491, 14303, 14293, 157259, 157253, 1525723, 4576997, 4576993, 4576991, 10411013, 33388093, 188332121, 194259301, 2853982501, 2853982499, 2853982477, 3913474277, 10883385143, 22809734971, 34883348389, 34883348369, 34883348341

Offset: 1

Author

Jean-Marc Rebert, Jul 23 2025

Keywords

• nonn
• base

Comments

Consecutive previous primes of the selected prime are ignored even though the may also have an identical count of digits.

Examples

			a(2) = 5, because the two primes in the sequence starting at 5, namely 5 and 7, each contain the same number of odd digits, and no earlier prime sequence meets this criterion.
In [2], each number contains 0 odd digits.
In [5, 7], each number contains 1 odd digit.
In [3, 5, 7], each number contains 1 odd digit.
In [11, 13, 17, 19], each number contains 2 odd digits.
In [97, 101, 103, 107, 109], each number contains 2 odd digits.
In [503, 509, 521, 523, 541, 547], each number contains 2 odd digits.
In [499, 503, 509, 521, 523, 541, 547], each number contains 2 odd digits.
In [491, 499, 503, 509, 521, 523, 541, 547], each number contains 2 odd digits.
In [14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389], each number contains 3 odd digits.
In [14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389], each number contains 3 odd digits.
		

Crossrefs

Cf. A000040, A196564,

Programs

Mathematica

oddn[n_] := Plus @@ Mod[IntegerDigits@ n, 2]; T = Table[0, {99}]; p = 1; While[p < 2  10^6, p = NextPrime[p]; c = oddn[p]; r=1; q=p; While[True, q = NextPrime[q]; If[oddn[q] == c, r++, Break[]]]; If[T[[r]] == 0, T[[r]] = p]]; Take[T, Position[T, 0][[1, 1]] - 1] (* Giovanni Resta, Jul 23 2025 *)

Extensions

More terms from Giovanni Resta, Jul 23 2025