A062209
Numbers k such that the smoothly undulating palindromic number (4*10^k-7)/33 = 121...21 is a prime (or PRP).
Original entry on oeis.org
7, 11, 43, 139, 627, 1399, 1597, 1979, 7809, 14059, 46499
Offset: 1
Patrick De Geest and Hans Rosenthal (Hans.Rosenthal(AT)t-online.de), Jun 15 2001
k=11 --> (12*10^11 - 21)/99 = 12121212121.
- J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 139, p. 48, Ellipses, Paris 2008.
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d[n_]:=IntegerDigits[n]; Length/@d[Select[NestList[FromDigits[Join[d[#],{2,1}]]&,1,1000],PrimeQ]] (* Jayanta Basu, May 25 2013 *)
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for(n=1,1e5,ispseudoprime(5^n<<(n+2)\33)&&print1(n",")) \\ M. F. Hasler, Jul 30 2015
A037487
Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,2.
Original entry on oeis.org
1, 12, 121, 1212, 12121, 121212, 1212121, 12121212, 121212121, 1212121212, 12121212121, 121212121212, 1212121212121, 12121212121212, 121212121212121, 1212121212121212, 12121212121212121, 121212121212121212, 1212121212121212121, 12121212121212121212
Offset: 1
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Table[FromDigits[PadRight[{},n,{1,2}]],{n,20}] (* or *) LinearRecurrence[ {10,1,-10},{1,12,121},20] (* Harvey P. Dale, Jun 21 2016 *)
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A037487(n)=10^n*4\33 \\ - M. F. Hasler, Jan 13 2013
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Vec(x*(2*x+1)/((x-1)*(x+1)*(10*x-1)) + O(x^100)) \\ Colin Barker, Apr 30 2014
A056803
Numbers k such that k copies of 12 followed by 1 is a palindromic prime.
Original entry on oeis.org
3, 5, 21, 69, 313, 699, 798, 989, 3904, 7029, 23249
Offset: 1
12121212121 is prime so 5 is a term.
Corresponding primes are given in
A092696. Corresponding decimal digit lengths are given in
A062209. a(k) = (
A062209(k-1)-1)/2.
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Do[m = n; If[PrimeQ[120(10^(2n) - 1)/99 + 1], Print[n]], {n, 1, 600}]
(IntegerLength[#]-1)/2&/@Select[10#+1&/@Table[FromDigits[Flatten[ IntegerDigits/@ PadRight[{},n,{1,2}]]],{n,2,15000,2}],PrimeQ] (* Harvey P. Dale, Apr 02 2020 *)
A153328
Numbers k such that (10^k-1)*120/99 + 1 is prime.
Original entry on oeis.org
6, 10, 42, 138, 626, 1398, 1596, 1978, 7808, 14058, 46498
Offset: 1
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/* n=number of values to test; r=repeat digits, e.g., 12, 121, 177, 1234; d = last digit appended to the end */
repr(n,r,d) = ln=length(Str(r));for(x=0,n,y=(10^(ln*x)-1)*10*r/ (10^ln-1)+1;if(ispseudoprime(y),print1(ln*x",")))
Showing 1-4 of 4 results.
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