A339541 -id:A339541 - cp's OEIS frontend

A339542 Primes p such that A339541(p) is prime.

2, 13, 19, 37, 71, 73, 127, 163, 167, 181, 271, 293, 307, 367, 431, 433, 457, 503, 569, 631, 659, 811, 907, 983, 1009, 1087, 1153, 1171, 1229, 1373, 1399, 1409, 1423, 1483, 1487, 1511, 1597, 1777, 1801, 1861, 1867, 1999, 2017, 2039, 2053, 2143, 2239, 2273, 2297, 2341, 2383, 2437, 2477, 2521, 2659

Offset: 1

J. M. Bergot and Robert Israel, Dec 08 2020

Primes p such that p + A138530(p, A007953(p)) is prime.

			a(5) = 71 is in the sequence because sod(71,10) = 8, sod(71,8) = 8 (since 71 = 107_8), and 71+8=79 is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007953, A138530, A339541.

sod:= proc(x,b) if b=1 then x else convert(convert(x,base,b),`+`) fi end proc:
select(p -> isprime(p+sod(p,sod(p,10))), [seq(ithprime(i),i=1..1000)]);

A339543 Beginnings of record-length chains of primes under iteration of A339541.

Original entry on oeis.org

1, 2, 1483, 2239, 3023417

Offset: 1

J. M. Bergot and Robert Israel, Dec 08 2020

A number n is in this sequence if the sequence defined by x(k+1) = A339541(k) with x(0)=n has more initial primes than the sequences for smaller n.

No more terms < 10^8.

			Starting with 1483 we get A339541(1483) = 1511, A339541(1511) = 1531, A339541(1531) = 1541, A339541(1541) = 1552.  This makes 4 initial primes (1483, 1511, 1531, 1541 but not 1552), which is more than we get starting with any number < 1483, so 1483 is in the sequence.

Cf. A339541, A339542.

sod:= (n.b) -> convert(convert(n,base,b),`+`):
f:= n -> n + sod(n, sod(n,10)):
g:= proc(n) option remember;
if isprime(n) then 1 + procname(f(n))
else 0
fi
end proc:
R:= 1: vmax:= 0: p:= 1:
while p < 10^7 do
  p:= nextprime(p);
  v:= g(p);
  if v > vmax then
   R:= R, p; vmax:= v;
  fi
od:
R;

cp's OEIS Frontend

A339542 Primes p such that A339541(p) is prime.

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