cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A087510 Primes consisting only of digits 0 and 1 occurring with equal frequency.

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%I A087510 #20 Sep 20 2024 14:52:46
%S A087510 10010101,10100011,1000011011,1000110101,1001000111,1001001011,
%T A087510 1001010011,1010000111,1010001101,1010010011,1010100011,1010110001,
%U A087510 1011000101,1100001101,1101001001,10000101011101,10000111100011,10000111110001,10001000011111,10001001011011
%N A087510 Primes consisting only of digits 0 and 1 occurring with equal frequency.
%C A087510 There are 18 digit pairs which can produce such primes: (1,0),(1,3),(1,4),(1,6),(1,7),(1,9),(2,3),(2,9),(3,4),(3,5),(3,7),(3,8),(4,7),(4,9),(5,9),(6,7),(7,9),(8,9).
%H A087510 Alois P. Heinz, <a href="/A087510/b087510.txt">Table of n, a(n) for n = 1..18167</a> (first 1000 terms from T. D. Noe)
%t A087510 Select[FromDigits/@Tuples[{0,1},14],PrimeQ[#] && Length[x=IntegerDigits[#]]==2*Count[x,0] &] (* _Jayanta Basu_, May 23 2013 *)
%o A087510 (PARI) \\ B(k,d1,d2,pred) k-digits of (d1,d2) each, satisfying pred.
%o A087510 B(k,d1,d2,pred)={my(L=List(),m=10^(2*k-1)); forsubset([2*k,k], s, my(t=(10^(2*k)-1)/9*d1 + (d2-d1)*sum(i=1, #s, 10^(s[i]-1))); if(t>=m && pred(t), listput(L,t))); vecsort(Vec(L))}
%o A087510 { concat(vector(7,k,B(k,0,1,isprime)))[1..20] } \\ _Andrew Howroyd_, Sep 20 2024
%Y A087510 Primes in A071925.
%Y A087510 The 18 sequences in this family are: this sequence (1,0), A087511 (1,3), A087512 (1,4), A087513 (1,6), A087514 (1,7), A087515 (1,9), A087527 (2,3), A087528 (2,9), A087529 (3,4), A087530 (3,5), A087531 (3,7), A087532 (3,8), A087533 (4,7), A087534 (4,9), A087535 (5,9), A087536 (6,7), A087537 (7,9), A087538 (8,9).
%K A087510 base,nonn
%O A087510 1,1
%A A087510 _Paul D. Hanna_ and _Amarnath Murthy_, Sep 11 2003