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a(1) = 1; thereafter a(n) is always the smallest integer > a(n-1) not leading to a contradiction, such that any four consecutive digits in the sequence sum up to a prime.
9

%I #9 Feb 04 2018 15:46:22

%S 1,2,3,5,7,8,9,51,83,110,111,211,301,310,311,631,703,710,911,2111,

%T 2113,2117,2119,2153,2155,2159,2171,2173,2177,2179,2513,2515,2519,

%U 2531,2533,2537,2539,2573,2575,2579,8513,8515,8519,8573,8579,8591

%N a(1) = 1; thereafter a(n) is always the smallest integer > a(n-1) not leading to a contradiction, such that any four consecutive digits in the sequence sum up to a prime.

%C Computed by Jean-Marc Falcoz.

%C From a(69)=1100110 onward starts a repeating pattern of length 54. - _M. F. Hasler_, Oct 16 2009

%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/ConsecDig.htm">Chiffres consecutifs dans quelques suites</a>

%H E. Angelini, <a href="/A152136/a152136.pdf">Chiffres consecutifs dans quelques suites</a> [Cached copy, with permission]

%o (PARI) A152604(n,show_all=0)={my(a);for(i=1,n,if( i<8,a=i+(i>3)+(i>4), my(l3d=if(a>99,a%1000,[789,951,183][i-7])); while( a++, my(t=a+l3d*10^#Str(a));forstep(d=#Str(a)-1,0,-1, isprime(sum(j=d,d+3,t\10^j%10)) & next; a+=10^d-a%10^d-1; next(2)); break)); show_all&print1(a", "));a} \\ _M. F. Hasler_, Oct 16 2009

%Y Cf. A158652, A152603..A152609.

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, Sep 23 2009