1,1

n is in the sequence iff the palindromic number 1(n).4.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n isn't of the forms 3m+1, 16m+11, 16m+12, 18m+11, 18m+15, etc. (the proof is easy).

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)

Makoto Kamada, Factorizations of 11...11411...11

a(n) = (A077780(n)-1)/2.

32 is in the sequence because the palindromic number (10^(2*32+1)+27*10^32-1)/9 = 1(32).4.1(32) =

11111111111111111111111111111111411111111111111111111111111111111 is prime.

Do[If[PrimeQ[(10^(2n + 1) + 27*10^n - 1)/9], Print[n]], {n, 2200}]

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A114633-A114647.

Sequence in context: A032815 A041053 A103108 this_sequence A141049 A052830 A041895

Adjacent sequences: A107121 A107122 A107123 this_sequence A107125 A107126 A107127

nonn

Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), May 19 2005