A143641 Odd prime-proof numbers (A118118) not ending in 5.

212159, 595631, 872897, 1203623, 1293671, 1566691, 1702357, 1830661, 3716213, 3964169, 4103917, 4134953, 4173921, 4310617, 4376703, 4586509, 4703801, 4749187, 4801387, 4928909, 5005353, 5051179, 5231739, 5258901, 5317573

Offset

1,1

Comments

Most "prime-proof" numbers are even or multiples of 5, cf. A118118.

Nicol & Selfridge proved that this sequence is infinite. - Charles R Greathouse IV, Jan 27 2014

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..3655 from Klaus Brockhaus)

Michael Filaseta, Mark Kozek, Charles Nicol and John Selfridge, Composites that remain composite after changing a digit, Journal of Combinatorics and Number Theory 2 (2011), pp. 25-36.

Project Euler, Problem 200: Prime-proof Squbes (2008).

Prog

(PARI) forstep( i=1, 10^7, 2, i%5 || next; isA118118(i) && print1(i", "))
(Magma) IsA143641:=function(n); D:=Intseq(n); return Intseq(n)[1] ne 5 and forall{ <k, j>: k in [1..#D], j in [0..9] | not IsPrime(Seqint(Insert(D, k, k, [j]))) }; end function; [ n: n in [1..4000000 by 2] | IsA143641(n) ]; // Klaus Brockhaus, Mar 03 2011
(Python)
from sympy import isprime
from itertools import count, islice
def selfplusneighs(n):
    s = str(n); d = "0123456789"; L = len(s)
    yield from (int(s[:i]+c+s[i+1:]) for c in d for i in range(L))
def agen():
    for n in count(1, 2):
        if n%5 == 0: continue
        if all(not isprime(k) for k in selfplusneighs(n)):
            yield n
print(list(islice(agen(), 8))) # Michael S. Branicky, Aug 16 2022

Crossrefs

Cf. A118118.

Sequence in context: A231418 A246999 A186694 * A184383 A234829 A184652

Adjacent sequences: A143638 A143639 A143640 * A143642 A143643 A143644

Keyword

base,nonn

Author

M. F. Hasler, Aug 27 2008, Sep 04 2008

Status

approved