A244268 Numbers n such that 1n2n3n4n5n6n7n8n9 is prime.

2, 10, 14, 59, 67, 89, 92, 113, 125, 134, 166, 169, 209, 211, 224, 239, 250, 286, 302, 307, 371, 379, 415, 421, 446, 512, 530, 550, 593, 602, 610, 625, 680, 701, 715, 758, 763, 785, 812, 814, 842, 901, 907, 932, 938, 1057, 1067, 1258, 1268, 1283, 1294, 1366, 1367, 1375, 1379, 1387, 1393, 1415, 1466

Offset

1,1

Comments

There are no numbers between 10^4 and 10^5. When n is five digits, 1n2n3n4n5n6n7n8n9 is divisible by 17.

Proof: First, 10000020000030000040000050000060000070000008000009 is divisible by 17. Thus we only need to consider 0n0n0n0n0n0n0n0n0 and see if it's divisible by 17. If it is, n0n0n0n0n0n0n0n must be. If n is five digits long, let n = 00001. We see that when n = 00001, n0n0n0n0n0n0n0n is divisible by 17. Since any five-digit number is a multiple of n (and has exactly 5 digits), all five-digit numbers will share the same property.

In general, for x = 0, 1, 2, ... if n is 16*x+5 digits long, then 1n2n3n4n5n6n7n8n9 is divisible by 17.

Links

Table of n, a(n) for n=1..59.

Example

1.10.2.10.3.10.4.10.5.10.6.10.7.10.8.10.9 = 1102103104105106107108109 is prime. Thus 10 is a member of this sequence.

Prog

(PARI) for(n=1, 10^4, b=""; for(i=3, 19, if(i==Mod(1, 2), b=concat(b, Str((i-1)/2))); if(i==Mod(0, 2), b=concat(b, Str(n)))); if(ispseudoprime(eval(b)), print1(n, ", ")))

Crossrefs

Sequence in context: A358749 A293931 A047043 * A233454 A065989 A299378

Adjacent sequences: A244265 A244266 A244267 * A244269 A244270 A244271

Keyword

nonn,base,less

Author

Derek Orr, Jun 24 2014

Status

approved