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A350832 a(n) is the least integer > 9 not listed earlier whose first two digits together with a(n-1)'s last two digits form two 2-digit primes when "read vertically in the same direction"; a(1) = 11. 1

%I #15 Jan 15 2023 18:43:02

%S 11,13,12,19,15,33,14,17,16,31,21,37,23,91,24,93,18,39,22,99,25,331,

%T 26,97,29,371,34,71,36,77,41,73,32,79,35,131,27,311,43,111,44,112,132,

%U 133,28,332,134,113,38,135,136,114,115,137,46,116,117,49,171,47

%N a(n) is the least integer > 9 not listed earlier whose first two digits together with a(n-1)'s last two digits form two 2-digit primes when "read vertically in the same direction"; a(1) = 11.

%C To explain "read vertically in the same direction": let b, c be the last two digits of a(n-1), and d, e the first two digits of a(n), then either both of 10b + d and 10c + e, or both of 10d + a and 10e + b must be primes > 9.

%C We are tempted to conjecture that this sequence contains all integers > 10 which don't have '0' as second or one of the last two digits.

%H √Čric Angelini, <a href="http://cinquantesignes.blogspot.com/2022/05/prime-bayonets.html">Prime bayonets</a>, personal web site "Cinquante signes" on blogspot.com, May 03 2022.

%e a(2) together with a(3) form the two 2-digit primes 11 and 23, when we write

%e a(2) = 13 and read the two last columns

%e a(3) = 12 both from bottom to top.

%e a(11) = 21 is followed by 37 and not 34 since we cannot write

%e a(11) = 21 and read one column downwards to get the prime 23

%e next = 34 and the other column upwards to get the prime 41.

%o (PARI) u=[a=11]; (ok(x,y)=isprime(x[1]*10+y[1])&&isprime(x[2]*10+y[2])); vector(99, n, if(a>u[1]+1, u=setunion(u, [a]), u[1]=a; while(#u>1 && u[2]==u[1]+1+(u[1]%10==9), u=u[^1])); a=digits(a)[-2..-1]; my(k=u[1], d); n>1&& until(k++%10 && k%100>9&& !setsearch(u, k) && (d=divrem(k\10^logint(k\10,10),10))[2]&& (ok(a,d)||ok(d,a)),); a=k)

%Y Cf. A350831 for a simpler single-digit variant.

%K nonn,base

%O 1,1

%A _M. F. Hasler_ and _Eric Angelini_, May 03 2022

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Last modified October 4 15:21 EDT 2023. Contains 365885 sequences. (Running on oeis4.)