A052078 -id:A052078 - 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

A052079 Concatenation of n consecutive ascending 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, 2, 0, 4, 15, 0, 7, 2, 0, 4, 129, 0, 5, 50, 0, 128, 3, 0, 23, 38, 0, 9998, 17, 0, 25, 2, 0, 16, 341, 0, 569, 42, 0, 14, 1203, 0, 2465, 102, 0, 212, 1161, 0, 197

Offset: 1

Patrick De Geest, Jan 15 2000

Next term a(44)=10^348-32 (only probable prime with 15324 digits). a(110)=9999968. If n is divisible by 22 then either a(n)=0 or a(n)=10^x-b for some bJens Kruse Andersen, Feb 03 2003

			For n = 7 we have a(7) = 7 so the seven consecutive ascending numbers 7,8,9,10,11,12 and 13 concatenated together gives the smallest possible prime of this form, 78910111213.

Carlos Rivera, Puzzle 78. The least prime by concatenating K consecutive integers, The Prime Puzzles and Problems Connection.

Cf. A030996, A052077, A052078, A052080.

isok(vc) = {my(x=""); for (i=1, #vc, x = concat(x, Str(vc[i]))); ispseudoprime(eval(x));}
a(n) = if (n % 3, for(i=1, oo, my(vc = vector(n, k, k+i-1)); if (isok(vc), return(i))), 0); \\ Michel Marcus, Mar 04 2021

Terms a(7)-a(43) 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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A052079 Concatenation of n consecutive ascending numbers starting from a(n) produces the smallest possible prime of this form, 0 if no such prime exists.

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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.

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Extensions