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A228144 Smallest k > n such that j*10^k + m*10^n - 1 is a prime number for at least a pair {j,m} with 0 < j < 10 and 0 < m < 10. 1
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 46, 47, 48, 49, 50, 51, 52, 53, 55, 55, 56, 57, 59, 59, 60, 61, 62, 63, 64, 66, 66, 67, 68, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The prime numbers are the sum of a near repdigit number starting with the digit j followed by k digits 0 and a nearepdigit number starting with the digit (m-1) followed by n digits 9 for m>1, or for m=1 a repdigit number with n digits 9.
The first primes are :
109, 1399, 13999, 139999, 1199999, 16999999, 289999999, 2099999999, 10999999999, 239999999999, 1099999999999, 34999999999999, 349999999999999, 2399999999999999.
Conjecture: there is always at least one k for each n.
LINKS
EXAMPLE
1*10^1+1*10^2=109 prime so a(1)=2.
PROG
PFGW & SCRIPTIFY
SCRIPT
DIM k
DIM j
DIM m
DIM n, 0
DIMS t
OPENFILEOUT myf, a(n, 3).txt
LABEL a
SET n, n+1
IF n>4000 THEN END
SET j, n
LABEL b
SET j, j+1
SET k, 0
LABEL c
SET k, k+1
IF k>9 THEN GOTO b
SET m, 0
LABEL d
SET m, m+1
IF m>9 THEN GOTO c
IF 4*(k+m)%3==1 THEN GOTO d
SETS t, %d, %d, %d, %d\,; n; k; j; m
PRP m*10^n+j*10^k-1, t
IF ISPRP THEN GOTO e
GOTO d
LABEL e
WRITE myf, t
GOTO a
CROSSREFS
Sequence in context: A246102 A243903 A296867 * A236841 A236850 A263028
KEYWORD
nonn
AUTHOR
Pierre CAMI, Aug 14 2013
STATUS
approved

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Last modified June 21 01:13 EDT 2024. Contains 373535 sequences. (Running on oeis4.)