A321568 Least prime p such that p plus the sum of its digits is the n-th prime after p.

11, 19, 37, 59, 97, 55787, 26699, 663959, 6974477, 86966771, 1095975857, 4649574977, 349685387573, 988839709939, 86396869388567

Offset

1,1

Comments

The other way round is not feasible because p minus the sum of its digits is never a prime but a multiple of 9.

Links

Table of n, a(n) for n=1..15.

Carlos Rivera, Puzzle 935. pi+SOD(pi)=p(i+n), The Prime Puzzles and Problems Connection.

Example

a(1) = 11 because 11 + 1 + 1 = 13 that is the first prime after 11.
a(2) = 19 because 19 + 1 + 9 = 29 that is the second prime after 19.

Maple

P:=proc(q) local a, b, c, d, n, x; x:=0; d:=[]; for n from 1 to q do
x:=nextprime(x); a:=x+convert(convert(x, base, 10), `+`);
if isprime(a) then c:=0; b:=x; while b<a do b:=nextprime(b); c:=c+1; od;
if numboccur(c, d)=0 then d:=[op(d), c]; lprint(c, x, a); fi; fi;
od; end: P(10^13); # Terms not in order.

Mathematica

Array[Block[{p = 2}, While[p + Total@ IntegerDigits@ p != NextPrime[p, #], p = NextPrime@ p]; p] &, 8] (* Michael De Vlieger, Dec 17 2018 *)

Crossrefs

Cf. A000040, A007953, A321569, A321570.

Sequence in context: A052368 A226542 A117873 * A271779 A271840 A076853

Adjacent sequences: A321565 A321566 A321567 * A321569 A321570 A321571

Keyword

base,nonn,more

Author

Paolo P. Lava, Dec 17 2018

Extensions

a(12)-a(15) from Giovanni Resta, Dec 17 2018

Status

approved