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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. 8
2, 11, 11, 277, 37783, 516493, 286330897, 286330897, 56676324799 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..9.

Carlos Rivera, Puzzle 163. P+SOD(P)

EXAMPLE

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.

MAPLE

with(numtheory);

A090009:=proc(q)

local a, b, c, d, j, n;

d:=0;

for n from 1 to q do

  a:=0; c:=ithprime(n); j:=c;

  while isprime(c) do

   a:=a+1; b:=0; while c>0 do b:=b+(c mod 10); c:=trunc(c/10); od;

   c:=j+b; j:=c; od;

   if a=d+1 then d:=a; lprint(d, ithprime(n)); j:=1;

   else if a>d+1 then for j from 1 to a-d do lprint(d+j, ithprime(n)); od; d:=a;

fi; fi; od; end:

A090009(10000000000); # Paolo P. Lava, Jun 07 2012

PROG

(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

CROSSREFS

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

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

Sequence in context: A292779 A245521 A275617 * A153706 A201187 A068225

Adjacent sequences:  A090006 A090007 A090008 * A090010 A090011 A090012

KEYWORD

base,more,nonn

AUTHOR

Joseph L. Pe, Jan 27 2004

EXTENSIONS

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

a(9) from Giovanni Resta, Jan 14 2013

STATUS

approved

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)