A086101 Numbers j such that the concatenation of the last digit of p(j) and the first digit of prime(j+1) is a prime.

1, 4, 5, 6, 7, 11, 20, 21, 25, 26, 27, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 42, 43, 44, 45, 63, 64, 66, 67, 68, 69, 73, 125, 126, 127, 128, 130, 131, 132, 133, 135, 136, 137, 154, 155, 156, 159, 160, 161, 163, 164, 165, 167, 168, 170, 172, 173, 174, 177, 178, 179

Offset: 1

Author

Zak Seidov, Jul 09 2003

Keywords

• easy
• nonn
• base

Comments

There are roughly 5/(18m log 10) * 10^m terms of this sequence up to 10^m: all primes between 10^k and 2*10^k, half the primes between 3*10^k and 4*10^k, 3/5 of the primes between 7*10^k and 8*10^k, and 1/4 of the primes between 9*10^k and 10*10^k for all 1 < k < m, using the prime number theorem in arithmetic progressions. Thus the "probability" that a random number up to 10^m is in this sequence is 0.12/m.

Examples

			20 is a term because prime(20)=71, prime(21)=73, and 17 is a prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

cldfdQ[{a_,b_}]:=PrimeQ[FromDigits[Join[{Mod[a,10]},{First[IntegerDigits[b]]}]]]; Position[ If[cldfdQ[#],1,0]&/@Partition[Prime[Range[200]],2,1],1]//Flatten (* Harvey P. Dale, Apr 26 2022 *)

Extensions

Comment from Charles R Greathouse IV, Apr 27 2010