A158125 Weakly prime numbers in the sense of A158124 but not A050249.

929573, 3070663, 5285767, 5974249, 7810223, 9262697, 9663683, 9700429, 10532453, 12968519, 19106729, 19158221, 19579907, 21825337, 23196157, 24328567, 29617897, 31181461, 31746383, 31839427, 36438379, 36745811, 37763641, 38585039, 38774851, 38888137, 39600559, 45412331, 45743483, 47500217, 47632271, 54127231, 56242891, 59816347

Offset: 1

Author

Eric W. Weisstein, Mar 13 2009

Keywords

• nonn
• base

Comments

A158124: initial digit may not be changed to a zero (and hence give a number with fewer digits).

A050249: initial digit may be changed to a zero.

For the following values 5, 6, 7, 8, 9, 10 of k, the number of terms < 10^k in this sequence is 0, 1, 8, 72, 589, 4977. - Jean-Marc Rebert, Nov 10 2015

Intersection of A227916 and A158124. So primes p that give another prime when the first digit is removed, but give a composite number when any one digit is modified in a way that does not change the digit count. - Jeppe Stig Nielsen, Jan 16 2022

Links

• Jean-Marc Rebert, Table of n, a(n) for n = 1..589
• Eric Weisstein's World of Mathematics, Weakly Prime

Crossrefs

Cf. A050249, A158124, A227916.

Programs

PARI

forprime(p=2,10^10,d=digits(p);!isprime(fromdigits(d[2..#d]))&&next();for(k=1,#d,for(j=(k==1),9,d[k]==j&&next();e=d;e[k]=j;isprime(fromdigits(e))&&next(3)));print1(p,", ")) \\ Jeppe Stig Nielsen, Jan 16 2022