A137716 Number of digits in the decimal expansion of the n-th Cullen prime.

1, 45, 1423, 1749, 1994, 5573, 9726, 9779, 17964, 27347, 79002, 108761, 145072, 407850, 1905090, 2010852

Offset: 1

Author

Ant King, Feb 09 2008

Keywords

• hard
• nonn
• base
• more

Comments

Cullen primes are prime numbers of the form k*2^k+1. This sequence is complete for all values of n up to 3500000.

Examples

			As the sixth Cullen prime, 18496*2^18496 + 1 = 1.311...*10^5572, is a 5573-digit number, we have a(6) = 5573.
		

Links

• Ray Ballinger and Mark Rodenkirch, Cullen Primes: Definition and Status.
• James Cullen, Question 15897, The Educational Times, Dec. 1905, p. 534.
• Allan Cunningham and H. J. Woodall, Factorisation of Q=(2^q ± q) and (q*2^q ± 1), The Messenger of Mathematics, Vol. 47 (1917-18), pp. 1-38.
• Wilfrid Keller, New Cullen Primes, Mathematics of Computation, Vol. 64, No. 212 (Ocober 1995), pp. 1733-1741.

Crossrefs

Cf. A055642, A005849, A002064.

Formula

a(n) = A055642(A050920(n)). [Corrected by Georg Fischer, Nov 18 2023]

Extensions

a(15)-a(16) from Amiram Eldar, Oct 27 2024