A232126 First element of the chain of primes ending in A232125(n), prime which cannot be extended to another prime by appending a digit, as it is the case of the other elements of the chain.

53, 5, 3, 2, 2, 3, 2, 2, 19, 103, 409, 1457011

Offset

0,1

Comments

See sequence A231426 for a variant using a similar concept "working forwards", i.e., the longest possible extension is looked for. See also A232127, A232128.

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = A232125(n)/10^n.

Example

a(0)=53 is the least prime that cannot be extended to another prime by appending some digit.
a(1)=5 is the least prime that can be extended ("once") to another prime, by appending the digit "3", such that the new prime cannot be extended further. (Indeed, 2 can be extended to 23 or 29, and 3 can be extended to 31 and 37, but all these allow at least one further extension to some prime, e.g., 233, 293, 311 and 373.)
a(3) = 2 is the first prime in the chain (2, 23, 239, 2393) where a digit is added 3 times to yield another prime, while adding any digit to the last term will give a composite. Here, 2393 is the least prime to occur in such a sequence of length 4=1+3.

Crossrefs

Sequence in context: A198776 A367821 A051320 * A078681 A143294 A143428

Adjacent sequences: A232123 A232124 A232125 * A232127 A232128 A232129

Keyword

nonn,base,more

Author

Michel Marcus and M. F. Hasler, Nov 19 2013

Status

approved