A328032 If there are m primes between 10^(n-1) and 10^n, a(n) is the middle prime if m is odd, otherwise the larger of the two middle primes.

5, 47, 509, 5273, 53047, 532907, 5356259, 53765519, 539119753, 5402600081, 54118210441, 541947386821, 5425907665571, 54313871643797, 543611236251491, 5440228524355381, 54438462600610513, 544705097744731559, 5449909581264135103

Offset

1,1

Comments

This sequence, unlike A309329, only contains primes.

For n > 2, a(n) > 10*a(n-1) for the terms shown. Does this continue?

The prime index of a(n): 3, 15, 97, 699, 5411, 44046, 371539, 3213018, 28304495, 252950023, 2286553663, 20862983416, 191836724429, 1775503643821, 16524756086736, 154541455728298, 1451397749344080, 13681755722697547, 129398810782042734, 1227438634918631724, 11674044544289825385, 111297278087667319110, 1063393839148059937607, 10180460079478002418395, 97640954583246485139774, 938046530135790455369642, 9025853588857058793877502, ..., .

Links

Table of n, a(n) for n=1..19.

Formula

a(n) is the next prime after A309329(n) - 1.

Example

a(1) is 5 since, among the single-digit primes, i.e., {2, 3, 5, 7}, the two middle primes are {3, 5}, of which the larger one is 5;
a(2) is 47 since it is the middle prime of the two-digit primes, i.e., {11, 13, 17, ..., 47, ..., 83, 89, 97};
a(3) is 509 since it is the middle prime of the three-digit primes, i.e., {101, 103, 107, ..., 509, ..., 983, 991, 997}.

Mathematica

f[n_] := Block[{p = PrimePi[ 10^(n -1)], q = PrimePi[ 10^n]}, Prime[ Ceiling[(q +p +1)/2]]]; Array[f, 13]

Crossrefs

Cf. A006879, A006880, A309329, A309359.

Sequence in context: A124450 A136023 A370100 * A074192 A058806 A302616

Adjacent sequences: A328029 A328030 A328031 * A328033 A328034 A328035

Keyword

nonn,hard

Author

Robert G. Wilson v, Oct 02 2019

Status

approved