A288212 Start with k=2*n, and until k+1 is prime, apply the map k -> k*(least prime factor of (k+1)); then a(n) = k+1, or 0 if k+1 never reaches a prime.

3, 5, 7, 1321, 11, 13, 43, 17, 19, 61, 23, 1321, 79, 29, 31, 97, 3571, 37, 571, 41, 43, 4621, 47, 337, 151, 53, 271, 21217561, 59, 61, 47059, 29761, 67, 1021, 71, 73, 223, 6917, 79, 241, 83, 421, 6221671, 89, 631, 277, 23971, 97, 1471, 101, 103, 313, 107, 109, 331

Offset

1,1

Comments

a(126) is unknown; it's known to either be 0 or have more than 152 digits.

a(126) has 277 digits. - J. Lowell, Jan 01 2023

a(161) is unknown; it is either 0 or has more than 333 digits. - J. Lowell and Sean A. Irvine, Feb 04 2023

Links

Sean A. Irvine, Table of n, a(n) for n = 1..160

Sean A. Irvine Java program (github)

Example

a(17) = 3571 because:
  34 + 1 = 35 is composite with smallest prime factor 5, and 34*5 = 170;
  170 + 1 = 171 is composite with smallest prime factor 3, and 170*3 = 510;
  510 + 1 = 511 is composite with smallest prime factor 7, and 510*7 = 3570;
  3570 + 1 = 3571 is prime.
The first term of A152466 that is one less than a prime is A152466(39); a(126) = A152466(39) + 1.
If A359444 has a term k that is one less than a prime, then a(161) = k + 1; otherwise, a(161) = 0.

Prog

(PARI) a(n) = {my(x = 2*n); while (! isprime(x+1), x = x*vecmin(factor(x+1)[, 1]); ); x+1; } \\ Michel Marcus, Jun 07 2017

Crossrefs

Cf. A152466, A359444.

Sequence in context: A065824 A191546 A069463 * A273010 A073691 A110336

Adjacent sequences: A288209 A288210 A288211 * A288213 A288214 A288215

Keyword

nonn

Author

J. Lowell, Jun 06 2017

Extensions

More terms from Michel Marcus, Jun 07 2017

Name simplified by Jon E. Schoenfield, Jan 01 2023

Status

approved