A244211 Integers n such that for every integer k>0, n*6^k-1 has a divisor in the set { 7, 13, 31, 37, 43 }.

133946, 213410, 299144, 33845, 367256, 803676, 1214450, 1250446, 1280460, 1704478, 1780150, 1792762, 1794864, 2003070, 2004962, 2203536, 2798489, 3014465, 3027709, 3041998, 3053350, 3194549, 3326301, 4244794

Offset

1,1

Comments

For n > 24 a(n) = a(n-24) + 4488211, the first 24 values are in the data.

When the number a(n) has 1 or 6 as the last digit, the number a(n)*6^k-1 is always divisible by 5 and always has another divisor in the set { 7, 13, 31, 37, 97 } for every k.

Links

Table of n, a(n) for n=1..24.

Formula

For n > 24, a(n) = a(n-24) + 4488211.

Prog

(PFGW & SCRIPT)
SCRIPT
DIM k, 1
DIM n
DIMS t
OPENFILEOUT myf, res.txt
LABEL loop1
SET k, k+1
SET n, 0
LABEL loop2
SET n, n+1
IF n>500 THEN GOTO a
IF (k*6^n-1)%7==0 THEN GOTO loop2
IF (k*6^n-1)%13==0 THEN GOTO loop2
IF (k*6^n-1)%31==0 THEN GOTO loop2
IF (k*6^n-1)%37==0 THEN GOTO loop2
IF (k*6^n-1)%43==0 THEN GOTO loop2
GOTO loop1
LABEL a
WRITE myf, k
PRINT k
GOTO loop1

Crossrefs

Cf. A076337, A243969, A244070, A244071, A244072, A244073, A244074, A244076.

Sequence in context: A023046 A034213 A226112 * A234206 A133528 A151940

Adjacent sequences: A244208 A244209 A244210 * A244212 A244213 A244214

Keyword

nonn

Author

Pierre CAMI, Jun 23 2014

Status

approved