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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
 11, 13, 12, 19, 15, 33, 14, 17, 16, 31, 21, 37, 23, 91, 24, 93, 18, 39, 22, 99, 25, 331, 26, 97, 29, 371, 34, 71, 36, 77, 41, 73, 32, 79, 35, 131, 27, 311, 43, 111, 44, 112, 132, 133, 28, 332, 134, 113, 38, 135, 136, 114, 115, 137, 46, 116, 117, 49, 171, 47 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. 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. LINKS Table of n, a(n) for n=1..60. Éric Angelini, Prime bayonets, personal web site "Cinquante signes" on blogspot.com, May 03 2022. EXAMPLE a(2) together with a(3) form the two 2-digit primes 11 and 23, when we write a(2) = 13 and read the two last columns a(3) = 12 both from bottom to top. a(11) = 21 is followed by 37 and not 34 since we cannot write a(11) = 21 and read one column downwards to get the prime 23 next = 34 and the other column upwards to get the prime 41. PROG (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) CROSSREFS Cf. A350831 for a simpler single-digit variant. Sequence in context: A112133 A052258 A036212 * A087551 A164076 A128509 Adjacent sequences: A350829 A350830 A350831 * A350833 A350834 A350835 KEYWORD nonn,base AUTHOR M. F. Hasler and Eric Angelini, May 03 2022 STATUS approved

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Last modified June 9 13:49 EDT 2023. Contains 363180 sequences. (Running on oeis4.)