A088785 Primes yielding other primes after each digit is incremented by 2 with carries ignored.

3, 5, 19, 29, 31, 37, 59, 61, 67, 83, 97, 127, 131, 137, 151, 157, 167, 191, 199, 211, 227, 241, 257, 277, 347, 359, 419, 421, 431, 449, 461, 479, 491, 521, 547, 587, 601, 607, 617, 631, 641, 661, 761, 797, 821, 829, 857, 859, 881, 883, 919, 941, 971, 977, 991

Offset

1,1

Comments

Imagine that each digit of a prime is on a wheel on a combination lock and each wheel is being rotated two notches. Thus for the digits 0 to 7, the replacement digit is simply the digit+2, but for 8 the replacement digit is 0 and for 9 the replacement digit is 1. Thus 227 --> 449 --> 661 --> 883 --> 5 (initial 0's are dropped on results).

Links

Table of n, a(n) for n=1..55.

Example

59 is a term because 5+2=7 and 9+2=1 (ignoring carry) and 71 is prime.

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def inc2(n): return int("".join(str((int(d)+2)%10) for d in str(n)))
def agen(): # generator of terms
    p = 2
    while True:
        if isprime(inc2(p)):
            yield p
        p = nextprime(p)
print(list(islice(agen(), 55))) # Michael S. Branicky, Jan 05 2022

Crossrefs

Cf. A088786, A088787, A088788.

Sequence in context: A095826 A058778 A211439 * A277688 A215131 A355253

Adjacent sequences: A088782 A088783 A088784 * A088786 A088787 A088788

Keyword

base,nonn

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 16 2003

Status

approved