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A244268 Numbers n such that 1n2n3n4n5n6n7n8n9 is prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A102340 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

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Last modified June 18 01:16 EDT 2021. Contains 345098 sequences. (Running on oeis4.)