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 A178613 The smaller member prime(i) of an emirp pair (prime(i),prime(j)), such that the digit sum of i equals the digit sum of j. 0

%I #9 Jun 26 2015 18:53:59

%S 37,359,769,1409,7687,10711,10853,11243,11593,13441,13751,14423,14551,

%T 14879,15307,15661,16879,17959,30853,31193,33863,34589,37307,37489,

%U 38449,73369,74959,75239,78259,78839,79669,90089,92779,100267,101531

%N The smaller member prime(i) of an emirp pair (prime(i),prime(j)), such that the digit sum of i equals the digit sum of j.

%C We consider base-10 emirp pairs (13,31) = (prime(6),prime(11)), (17,71) = (prime(7),prime(20)), (37,73) = (prime(12),prime(21)), ... (see A006567) and the digit sums of their prime indices (6,2=1+1), (7,2=2+0), (3=1+2,3=2=1),.. (see A156793).

%C If the digits sums of the two indices are the same, the smaller representative of the emirp pair is entered into the sequence.

%D W. W. R. Ball, H. S. M. Coxeter: Mathematical Recreations and Essays, 13th edition, Dover Publications, 2010

%D C. Mauduit, J. Rivat: Sur un problème de Gelfond: la somme des chiffres des nombres premiers, Annals of Mathematics, Vol. 171, No. 3, 1591-1646, 2010

%D H Schubart: Einfuehrung in die klassische und moderne Zahlentheorie Vieweg, Braunschweig, 1974

%e 37 = prime(12) and 73 = prime(21) are an emirp pair with equal digit sums of the indices 1+2 = 3 = 2+1, which puts 37 into the sequence.

%e 359 = prime(72) and 953 = prime(162) are an emirp pair with digit sums 7+2 = 9 = 1+6+2, which puts 359 into the sequence.

%e The 6th term is from the pair (10711 = prime(1306), 11701 = prime(1405)), see A033548

%e 16th term: (17959 = prime(2059), 95971 = prime(9250)).

%e 21st term: (34589 = prime(3694), 98543 = prime(9463)).

%t f[n_] := Plus @@ IntegerDigits@ PrimePi@n; fQ[n_] := Block[{id = IntegerDigits@n}, rid = Reverse@ id; q = FromDigits@ rid; rid != id && PrimeQ@ FromDigits@ rid && n < q && f@n == f@q]; lst = {}; p = 13; While[p < 102148, If[ fQ@p, AppendTo[lst, p]]; p = NextPrime@p]; lst (* _Robert G. Wilson v_, Jul 31 2010 *)

%Y Cf. A006567, A156793.

%K base,nonn

%O 1,1

%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 30 2010

%E More terms from _Robert G. Wilson v_, Jul 31 2010

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Last modified September 28 05:44 EDT 2023. Contains 365724 sequences. (Running on oeis4.)