A095180 Reverse digits of primes, append to sequence if result is a prime.

2, 3, 5, 7, 11, 31, 71, 13, 73, 17, 37, 97, 79, 101, 701, 311, 131, 941, 151, 751, 761, 971, 181, 191, 991, 113, 313, 733, 743, 353, 953, 373, 383, 983, 107, 907, 727, 337, 937, 347, 157, 757, 167, 967, 787, 797, 709, 919, 929, 739, 149, 359, 769, 179, 389, 199

Offset

1,1

Comments

Conjecture: the Benford law limit is 2=Sum[N[Log[10, 1 + 1/d[[n]]]], {n, 1, Length[d]}]^2/(( #totalprimes/#totalPrimes)). At 50000 primes total it is 2.05931. - Roger L. Bagula and Gary W. Adamson, Jul 02 2008

Presumably this does not satisfy Benford's law. - N. J. A. Sloane, Feb 09 2017

Links

Indranil Ghosh, Table of n, a(n) for n = 1..25000 (terms 1..206 from Roger L. Bagula and Gary W. Adamson)

Eric Weisstein's World of Mathematics, Benford's Law.

Index entries for sequences related to Benford's law

Example

The prime 107 in reverse is 701 which is prime.

Mathematica

b = Flatten[Table[If[PrimeQ[Sum[IntegerDigits[Prime[n]][[i]]*10^(i - 1), {i, 1, Length[IntegerDigits[Prime[n]]]}]], Sum[IntegerDigits[Prime[n]][[i]]*10^(i - 1), {i, 1, Length[IntegerDigits[Prime[n]]]}], {}], {n, 1, 1000}]] (* Roger L. Bagula and Gary W. Adamson, Jul 02 2008 *)
Select[FromDigits[Reverse[IntegerDigits[#]]]&/@Prime[Range[300]], PrimeQ] (* Harvey P. Dale, May 05 2015 *)

Prog

(PARI) r(n) = forprime(x=1, n, y=eval(rev(x)); if(isprime(y), print1(y", "))) \ Get the reverse of the input string rev(str) = { local(tmp, j, s); tmp = Vec(Str(str)); s=""; forstep(j=length(tmp), 1, -1, s=concat(s, tmp[j])); return(s) }
(Haskell)
a095180 n = a095180_list !! (n-1)
a095180_list =filter ((== 1) . a010051) a004087_list
-- Reinhard Zumkeller, Oct 14 2011

Crossrefs

Cf. A007500.

Cf. A004087, A010051.

Sequence in context: A104154 A123214 A119834 * A101989 A098922 A265324

Adjacent sequences: A095177 A095178 A095179 * A095181 A095182 A095183

Keyword

base,easy,nonn

Author

Cino Hilliard, Jun 21 2004

Status

approved