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A112013 Primes p such that there exists at least one number j and pi(p)= d_1 d_2 ... d_j*d_(j+1) d_(j+2) ... d_k where d_1 d_2 ...d_k is the decimal expansion of p. 3

%I #8 Feb 27 2013 10:06:42

%S 17,73,619,1117,64591,64601,64661,2077121,5070613,8883067,2121104897,

%T 4387047283,14304478789,503890508623,1547037000637

%N Primes p such that there exists at least one number j and pi(p)= d_1 d_2 ... d_j*d_(j+1) d_(j+2) ... d_k where d_1 d_2 ...d_k is the decimal expansion of p.

%C This sequence is the prime subsequence of the sequence A112012. There is no further term up to prime(26000000).

%C Contribution from _David Wasserman_, Mar 26 2009: (Start)

%C In all terms after 64661, d_(j+1) = 0.

%C No more terms < prime(822900000) (End)

%C a(16) > 2*10^12. - _Giovanni Resta_, Feb 27 2013

%e 8883067 is in the sequence because 8883067 is prime;

%e pi(8883067)=595161 & 595161=8883*067. Note that for this term j=4.

%t Do[If[MemberQ[h=IntegerDigits[Prime[m]];k=Length[h];Table[FromDigits[Table[h[[i]], {i, j}]]*FromDigits[Table[h[[i]], {i, j+1, k}]], {j, k}], m], Print[m]], {m, 26000000}]

%Y Cf. A112012.

%K base,more,nonn

%O 1,1

%A _Farideh Firoozbakht_, Oct 09 2005

%E More terms from _David Wasserman_, Mar 26 2009

%E a(14)-a(15) from _Giovanni Resta_, Feb 27 2013

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Last modified April 16 18:02 EDT 2024. Contains 371750 sequences. (Running on oeis4.)