A219251 -id:A219251 - cp's OEIS frontend

A182178 Beginning with 1, smallest positive integer not yet in the sequence such that two adjacent digits of the sequence (also ignoring commas between terms) sum to a prime.

1, 2, 3, 4, 7, 6, 5, 8, 9, 20, 21, 11, 12, 14, 16, 50, 23, 25, 29, 41, 43, 47, 49, 83, 85, 61, 65, 67, 411, 111, 112, 30, 32, 34, 38, 52, 56, 58, 92, 94, 70, 74, 76, 114, 98, 302, 116, 120, 202, 121, 123, 89, 203, 205, 207, 412, 125, 211, 129, 212, 141, 143

Offset: 1

Jim Nastos and Eric Angelini, Apr 16 2012

See A219110 for the numbers which do not occur in this sequence. See A219250 for the analog when "sum" is replaced with "absolute difference", and A219248-A219251 for related sequences. - M. F. Hasler, Apr 11 2013

			20 follows 9 since 9+2 and 2+0 is prime, and no number less than 20 (not already in the sequence) satisfies the stated property.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A182175, A182177.

a[1] = 1; a[n_] := a[n] = For[id = IntegerDigits[a[n-1]]; k = 1, True, k++, If[FreeQ[Array[a, n-1], k], dd = Join[id, IntegerDigits[k]]; If[And @@ PrimeQ /@ Plus @@@ Transpose[{Most[dd], Rest[dd]}], Return[k]]]]; Array[a, 62] (* Jean-François Alcover, Apr 17 2013 *)

A182178_vec={(n, a=[1], u=0)->while(#aM. F. Hasler, Apr 11 2013

A219250 Lexicographically earliest sequence of nonnegative integers such that the absolute difference of any two adjacent digits is prime.

Original entry on oeis.org

0, 2, 4, 1, 3, 5, 7, 9, 6, 8, 13, 14, 16, 18, 30, 20, 24, 25, 27, 29, 41, 31, 35, 36, 38, 50, 52, 42, 46, 47, 49, 61, 63, 53, 57, 58, 64, 68, 69, 70, 72, 74, 75, 79, 202, 92, 94, 96, 81, 83, 85, 86, 97, 203, 130, 205, 207, 241, 302, 413, 131, 303, 135, 242, 414, 136, 138, 141, 305, 246, 142, 416, 146, 147, 247, 249

Offset: 1

M. F. Hasler, Apr 11 2013

See A219249 for the version allowing only positive integers, i.e., starting with a(1)=1.
See A219248 (= range of A219250) for the numbers which occur in this sequence, and A219251 for the complement.
A182177 is the analog of this sequence for replacing "absolute difference" by "sum", A182178 is the same analog for A219249; A182175 is the analog of A219248 and A219110 corresponds to A219251.

M. F. Hasler in reply to E. Angelini, Re: Any digit-pair in S sums to a prime, SeqFan list, Apr 11 2013

PARI
```
{(n,a=[0],u=0)->while(#a
				
```

A182177 Beginning with 0, smallest positive integer not yet in the sequence such that two adjacent digits of the sequence (also ignoring commas between terms) sum to a prime.

Original entry on oeis.org

0, 2, 1, 4, 3, 8, 5, 6, 7, 41, 11, 12, 9, 20, 21, 14, 16, 50, 23, 25, 29, 43, 47, 49, 83, 85, 61, 65, 67, 411, 111, 112, 30, 32, 34, 38, 52, 56, 58, 92, 94, 70, 74, 76, 114, 98, 302, 116, 120, 202, 121, 123, 89, 203, 205, 207, 412, 125, 211, 129, 212, 141, 143, 214, 147, 414, 149, 216, 161, 165, 230, 232, 167, 416, 502, 303, 234, 305, 238, 307, 430, 250, 252, 320, 256, 503, 258, 321, 292, 323, 294, 325, 298, 329, 432, 341, 434, 343, 438, 347, 470, 349

Offset: 1

Jim Nastos and Eric Angelini, Apr 16 2012

A219250 is the analog of this sequence, replacing "sum" by "absolute difference". A219249 is the same analog for A182178. A219248 is the analog of A182175 and A219251 corresponds to A219110 = terms which do not occur in this sequence, i.e., the complement of its range. - M. F. Hasler, Apr 12 2013

			41 appears after 7 because 7+4 is prime and 4+1 is prime, and no other number less than 41 (not already in the sequence) satisfies this property. Example: 11 does not directly follow 7 since 7+1 is not prime.

Cf. A182175.

A182177_vec={(n, a=[0], u=0)->while(#aM. F. Hasler, Apr 11 2013

A219249 Lexicographically earliest sequence of positive integers such that the absolute difference of any two adjacent digits is prime.

Original entry on oeis.org

1, 3, 5, 2, 4, 6, 8, 13, 14, 7, 9, 20, 24, 16, 18, 30, 25, 27, 29, 41, 31, 35, 36, 38, 50, 52, 42, 46, 47, 49, 61, 63, 53, 57, 58, 64, 68, 69, 70, 72, 74, 75, 79, 202, 92, 94, 96, 81, 83, 85, 86, 97, 203, 130, 205, 207, 241, 302, 413, 131, 303, 135, 242, 414, 136, 138, 141, 305, 246, 142, 416, 146, 147, 247, 249, 250

Offset: 1

Eric Angelini and M. F. Hasler, Apr 11 2013

See A219250 for the version allowing nonnegative integers, i.e., starting with a(1)=0.

See A219248 for the numbers which occur in this sequence, and A219251 for the complement.

E. Angelini, Any digit-pair in S sums to a prime, SeqFan list, Apr 11 2013

Cf. A182175, A182177, A182178.

PARI
```
{A219249(n,a=[1],u=0)=while(#a
				
```

cp's OEIS Frontend

A182178 Beginning with 1, smallest positive integer not yet in the sequence such that two adjacent digits of the sequence (also ignoring commas between terms) sum to a prime.

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A219250 Lexicographically earliest sequence of nonnegative integers such that the absolute difference of any two adjacent digits is prime.

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PARI

A182177 Beginning with 0, smallest positive integer not yet in the sequence such that two adjacent digits of the sequence (also ignoring commas between terms) sum to a prime.

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Examples

Crossrefs

Programs

PARI

A219249 Lexicographically earliest sequence of positive integers such that the absolute difference of any two adjacent digits is prime.

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Programs

PARI