OFFSET
1,1
COMMENTS
The only palindrome in this sequence below 10^9 is 11 (per request of Giovanni Teofilatto). A004022 is a subsequence. - David A. Corneth, Jun 10 2016
If we have a concatenation of two palindromes A = A', B = B' which is palindromic, concat(A,B) =: A.B = (A.B)' = B'.A' = B.A, then A*(10^LB-1) = B*(10^LA-1) (LX = length of X) <=> A*R(LB) = B*R(LA), where R(n) = (10^n-1)/9. To have A.B prime we also must have gcd(A,B) = 1, thus A | R(LA) and B | R(LB). Such numbers are listed in A249647 (not A014950), the only palindromes there are of the form 1...1, 3...3 or 9...9. Thus the only palindromic terms in this sequence A273906 are the repunit primes A004022. - M. F. Hasler, Jun 10 2016
LINKS
David A. Corneth, Table of n, a(n) for n = 1..25912
David A. Corneth, PARI program
FORMULA
a(n) = A096489(n+1), n=1..21. - R. J. Mathar, Jun 12 2016. (This is a pure accident, I think, since A096489 is a finite sequence. - N. J. A. Sloane, Jun 12 2016)
EXAMPLE
The prime 1013 is a term since 101 and 3 are palindromic.
The prime 101 is not a term, since it is not a concatenation of two nonzero palindromic numbers.
The prime 131 is not a term because it is not a concatenation of two nonzero palindromic numbers.
MATHEMATICA
Take[#, 62] &@ Select[Sort@ Map[FromDigits@ Flatten@ IntegerDigits@ # &, Tuples[#, 2]], PrimeQ] &@ Select[Range[10^3], Reverse@ # == # &@ IntegerDigits@ # &] (* Michael De Vlieger, Jun 03 2016 *)
nxtPal[n_]:=With[{c=Join[{2}, Flatten[Table[{10*10^d, 11*10^d}, {d, 0, 10}]]]}, SelectFirst[n+c, PalindromeQ]]; Take[Join[{11}, Select[ #[[1]]*10^IntegerLength[ #[[2]]]+#[[2]]&/@ Flatten[{#, Reverse[#]}&/@Subsets[Join[Range[8], NestList[nxtPal, 9, 100]], {2}], 1], PrimeQ]//Union], 60] (* Harvey P. Dale, Dec 08 2024 *)
PROG
(PARI) \\ See program link from David A. Corneth, Jun 10 2016.
CROSSREFS
KEYWORD
nonn,easy,base,changed
AUTHOR
Giovanni Teofilatto, Jun 03 2016
EXTENSIONS
More terms from Michael De Vlieger, Jun 03 2016
STATUS
approved