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A089695 Numbers n such that placing as many possible '+' signs anywhere in between the digits yields a prime in every case. Let abcd... be the digits of n; then abcd, a + bcd, ab + cd, abc + d, a + b + cd, a + bc + d, ab + c + d, a + b + c + d, ... are all prime. 2
2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 227, 229, 281, 401, 443, 449, 467, 601, 607, 647, 661, 683, 809, 821, 863, 881, 4001, 4463, 4643, 6007, 6067, 6803, 8009 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Though the first 27 terms match those of A089392, the next term of A089392 (2221) is not a member of this sequence. Conjecture: sequence is finite.

No more terms < 10^8. - David Wasserman, Oct 04 2005

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

863 is a member 863, 8 + 63, 86 + 3, 8 + 6 + 3 are all prime.

MAPLE

with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1), j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1, op(i), d+1], i=choose([seq(j, j=2..d)]))]: for n from 10^(d-1) to 10^d-1 do sn:=convert(n, base, 10): fl:=0: for s in sch do m:=add(j, j=[seq(ds(sn[s[i]..s[i+1]-1]), i=1..nops(s)-1)]): if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ", n) fi od od: # C. Ronaldo

CROSSREFS

Cf. A089696.

Sequence in context: A129945 A046704 A089392 * A070027 A207294 A156658

Adjacent sequences:  A089692 A089693 A089694 * A089696 A089697 A089698

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Nov 10 2003

EXTENSIONS

Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004

STATUS

approved

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Last modified August 20 04:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)