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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 Pierre CAMI, Table of n, a(n) for n = 1..4000 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 Cf. A213790, A213883. Sequence in context: A246102 A243903 A296867 * A236841 A236850 A263028 Adjacent sequences: A228141 A228142 A228143 * A228145 A228146 A228147 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.)