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A273906 Primes equal to the concatenation of two nonzero palindromic numbers. 1
11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113, 199, 211, 223, 227, 229, 233, 277, 311, 331, 337, 433, 443, 449, 499, 557, 577, 599, 661, 677, 733, 773, 811, 877, 881, 883, 887, 911, 977, 991, 997, 1013, 1019, 1117, 1151, 1171, 1181 (list; graph; refs; listen; history; text; internal format)
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, 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 in the sequence because 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 *)
PROG
See PARI program link from David A. Corneth, Jun 10 2016.
CROSSREFS
Sequence in context: A140461 A120533 A226108 * A095862 A125845 A108871
KEYWORD
nonn,easy,base
AUTHOR
Giovanni Teofilatto, Jun 03 2016
EXTENSIONS
More terms from Michael De Vlieger, Jun 03 2016
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)