A052079 -id:A052079 - cp's OEIS frontend

A052077 Smallest prime formed by concatenating n consecutive increasing numbers, or 0 if no such prime exists.

2, 23, 0, 4567, 1516171819, 0, 78910111213, 23456789, 0, 45678910111213, 129130131132133134135136137138139, 0, 567891011121314151617, 5051525354555657585960616263, 0, 128129130131132133134135136137138139140141142143

Offset: 1

Patrick De Geest, Jan 15 2000

Starting numbers in concatenations are given by A052079.

Paolo P. Lava, Table of n, a(n) for n = 1..43
C. Rivera, Prime Puzzle 78.

Cf. A052078, A052079, A052080, A030997.

f[n_] := If[Mod[n, 3] == 0, 0, Block[{k = 1}, While[d = FromDigits@ Flatten@ IntegerDigits[ Range[k, k + n - 1]]; !PrimeQ@ d, k++]; d]]; Array[f, 16] (* Robert G. Wilson v, Jun 29 2012 *)

Terms a(7)-a(15) are calculated by Carlos Rivera and Felice Russo

a(16) from Max Alekseyev, Jan 31 2010

A052078 Smallest prime formed by concatenating n consecutive decreasing numbers, 0 if no such prime exists.

Original entry on oeis.org

2, 43, 0, 10987, 76543, 0, 73727170696867, 4645444342414039, 0, 56555453525150494847, 219218217216215214213212211210209, 0, 25242322212019181716151413, 6059585756555453525150494847, 0

Offset: 1

Patrick De Geest, Jan 15 2000

Starting numbers in concatenations are given by A052080.

If n is divisible by 3, a(n)=0. - Harvey P. Dale, Jun 03 2019

C. Rivera, Prime Puzzle 78

Cf. A052077, A052079, A052080.

Table[Min[Select[FromDigits[Flatten[IntegerDigits[#]]]&/@ Partition[ Range[ 1000,1,-1],n,1],PrimeQ]],{n,20}]/.\[Infinity]->0 (* Harvey P. Dale, Jun 03 2019 *)

Terms for n>6 calculated by Carlos Rivera and Felice Russo

A052080 Concatenation of n consecutive descending numbers starting from a(n) produces the smallest possible prime of this form, 0 if no such prime exists.

Original entry on oeis.org

2, 4, 0, 10, 7, 0, 73, 46, 0, 56, 219, 0, 25, 60, 0, 52, 117, 0, 535, 172, 0

Offset: 1

Patrick De Geest, Jan 15 2000

First hard cases occur for n = 22, 88 and 110.
a(22) = 10^1631 + 10 was found by James G. Merickel in Feb 2011.
a(88) = 10^14 + 6.
a(110) = 10^19 + 26 was found by Chris Nash.

			For n = 8 we have a(8) = 46 so the eight consecutive descending numbers 46,45,44,43,42,41,40 and 39 concatenated together gives the smallest possible prime of this form, 4645444342414039.

C. Rivera, Prime Puzzle 78

Cf. A052077, A052078, A052079.

Terms a(7)-a(21) calculated by Carlos Rivera and Felice Russo

cp's OEIS Frontend

A052077 Smallest prime formed by concatenating n consecutive increasing numbers, or 0 if no such prime exists.

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A052078 Smallest prime formed by concatenating n consecutive decreasing numbers, 0 if no such prime exists.

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Author

Keywords

Comments

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Crossrefs

Programs

Mathematica

Extensions

A052080 Concatenation of n consecutive descending numbers starting from a(n) produces the smallest possible prime of this form, 0 if no such prime exists.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions