A090009 Begins the earliest length-n chain of primes such that any term in the chain equals the previous term increased by the sum of its digits.

2, 11, 11, 277, 37783, 516493, 286330897, 286330897, 56676324799

Offset: 1

Author

Joseph L. Pe, Jan 27 2004

Keywords

• base
• more
• nonn

Comments

From the second term on, subsequence of A[2] := A048519. Due to the "exclusive" definition of this sequence, A048523(1) > a(2), but for k >= 3, a(k) = A[k](1) for A[3..9] = A048524 .. A048527, A320878 .. A320880. - M. F. Hasler, Nov 09 2018

Examples

			11 begins the earliest chain 11, 13, 17 of three primes such that any term in the chain equals the previous term increased by the sum of its digits, viz., 13 = 11 + 2, 17 = 13 + 4. Hence a(3) = 11.
		

Links

• Carlos Rivera, Puzzle 163. P+SOD(P)

Crossrefs

Cf. A047791, A048519, A062028 (n + digit sum of n).

Cf. A048523 .. A048527, A320878 .. A320880.

Programs

PARI

A090009(n,P=2)=forprime(p=P,,P=p;for(i=2,n,isprime(P=A062028(P))||next(2));return(p))
P=0; A090009_vec=vector(6,n,P=A090009(n,P)) \\ Takes long for n > 6. - M. F. Hasler, Nov 09 2018

Extensions

a(7)-a(8) from Donovan Johnson, Jan 08 2013

a(9) from Giovanni Resta, Jan 14 2013